Heat a large skillet over medium-high heat. Add 1 tablespoon of butter or olive oil and sauté the cubed chicken until barely cooked through, about 5-7 minutes. Remove from skillet and set aside.
Lower the heat to medium, add the remaining butter or oil, and cook the diced onions, carrots, and celery until softened, about 5 minutes.
Stir in the thyme and pour in the chicken stock or broth. Simmer until the vegetables are tender, about 10 minutes.
Meanwhile, cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a small bowl, mix the cornstarch with a little water to dissolve. Add the heavy cream and the cornstarch mixture to the skillet, stirring until the sauce thickens.
Add the sautéed chicken and frozen peas to the skillet, stirring gently until heated through, about 2-3 minutes.
Mix in the drained penne pasta, stirring until well coated in the sauce. Adjust seasoning with salt and pepper to taste.
Serve warm, garnished with chopped parsley if desired.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3 days.