Pound chicken to an even thickness between plastic wrap using a meat mallet. Season with salt and pepper, if desired.
Melt 2 tablespoon butter in a large nonstick skillet over medium heat; add half of chicken and cook 3 to 4 minutes per side or until done. Remove from skillet. Repeat with 2 Tbsp butter and remaining chicken.
Melt 1 tablespoon butter in skillet over medium heat; add shallot, garlic, Italian seasoning, and pepper. Cook, stirring constantly, 1 minute. Add tomato paste; cook, stirring, 2 minutes.