Melt the butter over medium heat in a heavy skillet. Add the onion and garlic and sauté until translucent, about 4 minutes.
Add the mushrooms and cook until they release their liquid and begin to brown, about 10 minutes. Add the thyme, zest, and wine; simmer until the liquid is reduced by half, about 5 minutes.
Add the broth, bring to a boil, and simmer 5 minutes. Stir in the cream, salt, and pepper. Simmer until the sauce lightly coats the back of a spoon.