Heat a large skillet over medium-high heat. Add 2 tablespoons vegetable oil, swirling to coat.
Season chicken with salt and pepper. Add to the hot skillet, and cook for 10-12 minutes, turning halfway, until the chicken is mostly cooked through. Remove from the heat and cover with foil to keep warm.
In a the same skillet melt the butter over medium-high heat and sauté garlic for 1-2 minutes, until you can start to smell it.
Add in flour, stir and cook for a couple minutes until no white streaks remain.
Slowly whisk in heavy cream and milk and bring the mixture to a simmer. Cook for 5-6 minutes until it starts to thicken.
Add thawed spinach and diced artichoke hearts. Cook 2 to 3 minutes or until heated through.
Stir in Parmesan cheese and season with salt and pepper.