Clean mushrooms with a damp cloth to remove debris and slice into uniform pieces.
Pulse cauliflower florets in a food processor until they reach a coarse, rice-like consistency.
Heat olive oil and 1 tablespoon of butter in a large heavy-bottomed skillet over medium-high heat.
Add mushrooms to the skillet in a single layer and sauté without stirring for 3 minutes to develop a brown crust.
Stir mushrooms and continue cooking for 4 minutes until moisture has evaporated and mushrooms are tender.
Incorporate the remaining 1 tablespoon of butter and the cauliflower crumbles into the skillet.
Sauté the mixture for 5 minutes, stirring frequently, until cauliflower is tender and slightly caramelized.
Add minced garlic and thyme; cook for 60 seconds until aromatic.
Season with salt and black pepper to taste.
Remove from heat and garnish with chopped parsley before serving.