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Export 10 ingredients for grocery delivery
Peel zucchini lengthwise with a vegetable peeler to create long strips.
Lay zucchini strips flat on a paper towel-lined baking sheet; set aside to dry.
Heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat.
Season chicken breasts with thyme, salt and pepper; add to skillet and cook for 4 minutes per side, or until cooked through.
Remove from skillet; cut into strips and set aside. Cover to keep warm.
In the same skillet, heat the butter and olive oil over medium heat.
Add garlic and tomato paste and cook for 30 seconds, or until fragrant.
Stir in diced tomatoes and bring to a boil; reduce heat and simmer gently for 10 minutes.
Add the vodka and simmer for 8 to 10 minutes.
Stir in milk and continue to simmer for 10 more minutes.
Stir in the cheese; continue to stir until well incorporated.
Add previously prepared chicken and zucchini to the sauce; cook for 1 more minute, or until heated through.
Remove from heat and serve.