Heat oven to 400°F and line a cookie sheet with foil. Combine the sliced mushrooms, minced garlic, rosemary, walnuts, and smoked paprika in a small dish and drizzle with olive oil. Toss to coat and season with salt.
Spread the mixture evenly on the cookie sheet and roast in the oven for 15 minutes.
Process one head of cauliflower florets in a food processor by pulsing until very fine.
Steam the processed cauliflower in a medium pot, covered, with ½ cup water for 5 minutes or until the mixture is slightly tender. You don’t want it to be too soft since it will need to resemble grits.
Pour half and half into the cauliflower grits, stir and simmer on medium-low heat for 3 minutes. This is just enough time to heat the milk.
Stir in the sharp cheddar and butter and reduce heat to low until the mixture is creamy and well combined. Season with salt to taste. If you like your grits runny add another ¼ c. water.
Remove roasting pan from the oven once your mushrooms are soft and the edges are a deep brown.
Serve the cauliflower grits hot, topped with the mushroom mixture and extra butter if desired!