Preheat oven to 400 degrees F (205 degrees C).
Cut the whole head of garlic in half, drizzle on about 2 tablespoon oil over the cut sides, place the garlic top back onto the bottom and wrap the garlic head with aluminum foil and place on your small baking sheet.
Arrange mushrooms onto the small baking sheet and pour butter over them. Put the baking sheet into the oven for 40 minutes, or until the mushrooms are roasted and golden brown. Pull out and set aside.
***OR saute the mushrooms in your frying pan in 2 tablespoon oil over medium heat for 7-8 minutes before Step 6.
Begin boiling a large pot of salted water around the end of the mushroom's roasting time. Add in the pasta after cooking your mushrooms and cook to al dente (or just under al dente) according to package directions.
In a cast iron pan or frying pan, heat up the rest of the oil along with the lemon zest, red pepper flakes, and fresh thyme over medium-low heat.
After a minute or two, add in the minced garlic cloves, stirring with a wooden spoon or heat resistant spatula to ensure the garlic doesn't burn. Cook the garlic for about one minute, it should be very fragrant. Take the pan off the heat.
Add the lemon juice to your pan, then add the cooked pasta and about ½ cup of pasta water. Add in the parmesan cheese. Toss the pasta and sauce together with tongs to mix everything together well.
Add in the roasted mushrooms and squeeze cloves of the roasted garlic into the pan, if using. Toss thoroughly again.
Taste and season with kosher salt and freshly cracked black pepper as needed.
To serve, plate the pasta with creamy mushroom sauce and add a ball of burrata (or tear apart a couple of large ones) over each serving. The cream inside the burrata will add more creaminess to your plates of pasta.