Heat butter in a large, deep skillet over medium heat. Cook and stir mushrooms, 1/2 cup white wine, and 1 clove minced garlic until liquid has reduced and mushrooms have softened, about 5 minutes. Remove from heat and place in a bowl.

Heat the same skillet over medium-high heat. Cook and stir Italian sausage in the hot skillet until browned and crumbly, 5 to 7 minutes, dividing it into bite-sized portions while stirring. Remove excess grease by placing paper towels onto a plate and dumping browned sausage onto it to drain. Return sausage to the skillet.

Return cooked mushrooms back to the skillet with sausage and add tortellini, Alfredo basil sauce, remaining 1/2 cup white wine, and remaining garlic. Reduce heat to medium-low. Cover and cook, stirring occasionally, for about 10 minutes.