Place the butter in a large cast-iron skillet over medium-high heat.
Cook, whisking, until brown (but not black!) flecks appear—this is browned butter.
Reserve ¼ cup for drizzling over the top of the cupcakes before serving. (Note: If using bacon fat or lard, simply heat the fat in the skillet before continuing with Step 3.)
Add the mushrooms, celery, onions, sage, and poultry seasoning to the skillet with the browned butter and sauté until tender and translucent, about 5 minutes.
Add the sausage and sauté, using a wooden spoon to break up the pieces, until the meat is cooked through and no longer pink, about 4 minutes.
While the meat is cooking, cut the buns into ½-inch cubes.
Add the bread cubes to the pan with the sausage mixture.
Pour in the broth and mix well.
Season with salt and pepper. Slide the pan off the heat and stir in the beaten eggs.
Pour the mixture into the greased muffin pan, filling each well about three-quarters full.
Bake the keto stuffed mushrooms cupcakes, covered, for 15 to 20 minutes, until cooked through.
Uncover and bake for 5 more minutes, until the cupcakes are golden brown on the top.
Drizzle the reserved ¼ cup of browned butter over the tops of the cupcakes and serve