Place chicken breasts between plastic wrap and pound to an even ¾-inch thickness. Pat thoroughly dry with paper towels.
Combine Cajun seasoning, salt (if using), and black pepper in a small bowl. Sprinkle evenly over both sides of the chicken breasts, pressing gently to adhere.
Allow the seasoned chicken to rest at room temperature for 15-20 minutes.
Heat a skillet over medium-high heat and add the oil. Heat until shimmering but not smoking (approximately 350°F).
Place chicken breasts in the hot skillet, presentation side down. Cook undisturbed for 4-5 minutes until a deep golden crust forms.
Turn chicken and cook for an additional 4-5 minutes on the second side until internal temperature reaches approximately 155-160°F.
Transfer chicken to a plate and tent loosely with foil to keep warm.
Reduce heat to medium-low and add butter to the same skillet. Once melted, add garlic and shallot, cooking for 1-2 minutes until fragrant.
Add chicken stock, scraping up all browned bits from pan bottom. Simmer until reduced by half, approximately 2-3 minutes.
Reduce heat to low and slowly whisk in the heavy cream. Simmer gently for 3-4 minutes until sauce begins to thicken slightly.
Whisk in tomato paste, lemon juice, cayenne (if using), and half the herbs. Simmer for an additional 2 minutes.
Return chicken breasts to the skillet, including any accumulated juices. Spoon sauce over the chicken and simmer for 1-2 minutes to reheat.
Verify chicken has reached a safe internal temperature of 165°F.
Serve chicken topped with additional sauce and remaining fresh herbs.