Will'S Mushrooms

Heat the oven to 375 degrees. Using a damp towel, gently wipe the mushroom caps clean. Arrange them with their gills down on an ovenproof rack set on top of a rimmed baking sheet. Bake the mushrooms for about 15 minutes, until they start to shrink and become tender, releasing a good amount of liquid onto the baking sheet below. Carefully remove the mushrooms from the oven and pour off the liquid, wiping the baking sheet dry. Flip the mushroom caps over and arrange them on the baking sheet again. Turn the oven up to 475 degrees.
Put the bacon in a small skillet over medium heat. Cook, stirring occasionally, until the bacon has rendered most of its fat and starts to become crisp, about 5 minutes. Add the shallot and continue to cook, stirring frequently, until the shallot is translucent and lightly caramelized, another 5 to 7 minutes. Using a slotted spoon, transfer the bacon and shallots to a medium bowl, discarding the bacon fat in the pan.
Add the rest of the ingredients to the bowl and stir gently to combine. (You probably won't want to add any salt, but now's the time to taste just in case.) Top each mushroom cap with about a quarter of the mixture, smoothing it so that it almost reaches the edges. Return the mushrooms to the oven and bake until the cheese starts to brown and bubble, 10 to 15 minutes. Let the mushrooms cool for a few minutes before serving.