1 Tablespoon Olive Oil
2 Tablespoons Butter
4 Medium Yellow Onions, Peeled and Sliced
1 teaspoon Salt
1 1/2 Pounds Mushrooms
6 Cloves Garlic, Minced
1/2 C White Wine
1 1/2 Pounds Chicken Breast
1/4 C Butter
1/4 C Flour
3 C Whole Milk
6 Ounces Asiago Cheese
1 teaspoon Salt
1/2 teaspoon Black Pepper
1/2 Cup Fresh Basil Leaves, chopped
16 Ounces Pasta
Combine olive oil and 2T butter in a large pot over medium heat. Add the sliced onions and salt and cook until caramelized and deep brown, about 30 - 45 minutes, stirring frequently. Turn the heat down as needed to keep the onions from scorching.
Meanwhile, wash and slice mushrooms and mince garlic. Cook chicken breasts till browned on both sides and juices run clear. Slice chicken into bit-sized pieces.
When onions have finished caramelizing, add mushrooms and garlic and cook until mushrooms are soft, about 5 - 10 minutes. Add the wine and cook over medium-high heat until liquid is mostly evaporated.
While the mushrooms cook, prepare pasta according to package instructions.
To make the cream sauce, melt 1/4 C Butter in a small saucepan over medium heat. Add the flour and whisk to combine. Cook and stir for 2 to 3 minutes, then slowly add the milk, whisking vigorously to prevent lumps from forming. Cook over medium-low heat until thickened, about 5 minutes. Remove from heat and add asiago cheese in batches, stirring to melt. Add salt and pepper to taste.
When the liquid has mostly evaporated from the mushrooms, add the cream sauce and the chicken and stir to combine. Heat over low heat for 2 - 3 minutes. Just before serving, stir in chopped fresh basil leaves.
Serve over cooked pasta noodles.