Mushroom Asiago Rabbit

1 lb boneless skinless rabbit strips
salt and pepper
½ cup all-purpose flour
4 Tbsp unsalted butter
1 lb sliced mushrooms
½ tsp salt
3 cloves garlic, minced
½ cup dry white wine or chicken broth
¾ cup low-sodium chicken broth
3 sprigs fresh thyme or ¾ tsp dried thyme leaves
½ cup heavy cream
½ cup shredded Asiago cheese
Parmesan cheese for sprinkling

Cover the rabbit pieces with a sheet of plastic wrap and pound with a meat mallet or the bottom of a small skillet until all of the pieces are about ¼" thick. Lightly season each cutlet on both sides with salt and pepper and dredge in flour, shaking off any excess.
Place a large skillet over medium-high heat and melt about 2 Tbsp unsalted butter. Add as many cutlets as will fit comfortably into the skillet, but be sure not to overcrowd the pan. Sauté for about 5 minutes until golden brown on the first side, then flip and cook for 1 additional minute. Remove the rabbit from the skillet to a plate and cover lightly with foil. Repeat with remaining rabbit strips, removing and covering when cooked.
Add remaining butter to the skillet along with the mushrooms and ½ tsp salt. Cook for 10 minutes, stirring occasionally, until the mushrooms are golden brown and become softened. Add garlic and cook for an additional 2 minutes.
Pour white wine (or ½ cup chicken broth) into the skillet and stir to scrape up anything that is sticking to the bottom of the pan. Once the wine has nearly all evaporated, add ¾ cup chicken broth and thyme. Bring the mixture to a boil, reduce heat to medium and cook for 10–15 minutes at a rapid simmer until the liquid is reduced by half.
Reduce heat to medium-low and stir in heavy cream. Sprinkle the Asiago cheese over the top of the sauce and stir constantly until the cheese melts. Nestle the rabbit strips back into the skillet and allow it to simmer in the sauce just until  heated through and the sauce has slightly thickened. Sprinkle with a bit of Parmesan cheese and serve right away, either all by itself, or spooned over pasta or mashed potatoes. Enjoy!