In a large bowl, toss together mushrooms, oil, salt, and pepper. Place on prepared pan; bake for 20 minutes.
Meanwhile, in a large saucepan, bring broth to a boil over medium-high heat. Add grits, whisking to combine. Reduce heat to low; cover and cook for 20 minutes, stirring occasionally. Remove from heat; stir in mozzarella, Cheddar, and half-and-half. Cover until ready to use.
In a medium saucepan, melt butter over medium heat. Cook until butter turns a medium-brown color and has a nutty aroma, about 10 minutes. Remove from heat; add lemon juice, garlic, and thyme. Stir in mushrooms. Layer cheese grits and mushroom mixture in serving glasses. Garnish with thyme, if desired.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/browned-butter-mushroom-and-cheese-grits-parfaits-recipe/