Prep chicken breasts by slicing into 1/2-inch-thick cutlets and season with salt, pepper, and 1/2 tsp Italian seasoning.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high heat until hot.
Sear chicken in the skillet for 4-5 minutes per side, or until golden brown and cooked through.
Set chicken aside on a plate and remove skillet from heat momentarily.
Add minced garlic to the pan (save a small portion for later) and sauté for 20-30 seconds until fragrant.
Reduce heat to medium. Return skillet to the stove and add the remaining butter, then stir until melted.
Gradually whisk in heavy cream and bring the mixture to a gentle simmer.
Stir in freshly grated Parmesan cheese until melted and smooth (add reserved garlic, if using).
Season with remaining Italian seasoning, salt, and black pepper to taste.
While sauce is simmering, cook fettuccine in a large pot of salted boiling water until al dente (follow package directions). Reserve a small portion of pasta cooking water for adjusting sauce consistency.
Add cooked pasta to the skillet and toss to coat with the sauce. If the sauce is too thick, add a splash of reserved pasta water until desired consistency is achieved.
Divide chicken into portions and place on plates with pasta. Serve immediately.