Step 1

Peel zucchini lengthwise with a vegetable peeler to create long strips.

Step 2

Lay zucchini strips flat on a paper towel-lined baking sheet; set aside to dry.

Step 3

Heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat.

Step 4

Season chicken breasts with thyme, salt and pepper; add to skillet and cook for 4 minutes per side, or until cooked through.

Step 5

Remove from skillet; cut into strips and set aside. Cover to keep warm.

Step 6

In the same skillet, heat the butter and olive oil over medium heat.

Step 7

Add garlic and tomato paste and cook for 30 seconds, or until fragrant.

Step 8

Stir in diced tomatoes and bring to a boil; reduce heat and simmer gently for 10 minutes.

Step 9

Add the vodka and simmer for 8 to 10 minutes.

Step 10

Stir in milk and continue to simmer for 10 more minutes.

Step 11

Stir in the cheese; continue to stir until well incorporated.

Step 12

Add previously prepared chicken and zucchini to the sauce; cook for 1 more minute, or until heated through.

Step 13

Remove from heat and serve.