Procedure
Prepare the dough: Combine water, sugar, and yeast in the bowl of your stand mixer and stir together gently. Allow to bloom for 5 minutes. Fit the stand mixer with a dough hook and turn on low; gradually incorporate flour, then 2 tablespoons olive oil, then 1/2 tsp kosher salt.
Turn stand mixer up to medium-high and knead for 5 minutes. Dough should pull completely away from the sides of the bowl while the dough hook is spinning, but feel a bit sticky when touched or when not in motion. If the dough seems too dry, add 1 tsp water, or if the dough seems excessively sticky and is not coming together, add 1–2 tsp flour. Knead for an additional 2–3 minutes.
Shape the dough into a ball with your hands. Drizzle a small amount of the extra olive oil into the bowl, add the dough ball, and rub some of the oil on top. Place in a warm spot and cover with plastic wrap or a wet tea towel and allow to rest for 1 hour, or until the ball has doubled in size.
In the meantime, prep the cheddar. Grate roughly one-third of the dairy bar with a box grater. Set grated cheese aside. Break down the remaining cheese into small chunks, about 1/4-inch to 1/2-inch in size; you could cut them into cubes or just use the tip of a small knife to break pieces off. Place cheese chunks in the fridge until needed.
Second rest: Line a 7x11-inch (2 quart) baking dish with parchment paper and coat with a bit of the extra olive oil. Sprinkle the grated cheddar into the bottom of the dish.
Scoop the dough out of the bowl and press out the excess air. Divide the dough in half. Stretch each half into the shape of a rectangle that is slightly smaller than the baking dish; note that the dough will expand so it does not need to fill the size of the whole dish yet. Place one half over the grated cheddar in the dish. Keep the other half on a separate piece of parchment paper that has been lightly oiled with the olive oil.
Cover both halves with plastic wrap or a wet tea towel and allow to rest for 1 hour.
Prepare the filling: While the dough is resting, pan roast the mushrooms and caramelize the onions. Heat a large non-stick skillet on medium. Reserve a few mushrooms for decoration and add the rest to the dry pan. Sauté until the volume is reduced to about two-thirds of the original and the mushrooms are squeaky as you move them around with a spatula. Remove the mushrooms from the pan.
Add the butter to the pan, then add the onion slices. Reduce the heat to low once you notice the color becoming more vibrant. Cook the onions until they are tender and start to brown on the edges, about 10 minutes.
Add the mushrooms back to the pan, as well as 1/4 teaspoon kosher salt. Turn the heat back up to medium. Stir often to encourage evaporation, and cook until the mushrooms seem to have released their excess moisture, about 7 minutes. Remove from heat and allow to cool until the dough is done resting.
Once the dough has completed its second rest, the bottom half should be able to be stretched to fill the bottom of the pan. Shape as needed. Then add about one-third of the sweet potato slices to the pan, followed by most of the cheddar chunks, followed by the mushroom and onion mixture.
Third rest: Place the other half of the dough on top of the mushrooms. Press the two halves of dough along the edges to seal shut and tuck them under, though this does not need to be perfect. Allow to rest, covered, for an additional 20 minutes.
Meanwhile, preheat the oven to 400°F.
Decorate the top of the bread and bake: Press the remaining cheddar chunks into the surface of the bread. Press your fingers into the dough to form additional dimples.
To make a sweet potato rose, cut a slice of sweet potato in half and roll into a tight spiral. Roll the other half around the first. Place this firmly into the surface of the dough where you want the center of the rose to be. Starting with the smallest slices of sweet potato available, firmly insert slices around the rose’s center to form petals. Select gradually larger sweet potato slices and keep adding them as petals until the desired size is achieved.
Repeat to form other roses as desired. (You may not end up using all the sweet potato).
Add vegetable leaves and mushrooms to complete your decoration. Brush everything with a generous layer of olive oil. Sprinkle the remaining 1/4 teaspoon kosher salt over the top.
Bake for 35–40 minutes or until the top is a light brown. Note that after 30 minutes, you may wish to check on your decoration and add small pieces of foil over the parts of the sweet potato that have darkened, to prevent burning.
Carefully lift the bread out of the pan via the parchment paper and allow to set for a couple minutes before slicing and enjoying!
