Pat dry chicken thighs. Immediately before searing, coat with olive oil and seasoning. For best crispy-skin results, place the chicken on a wire rack and refrigerate uncovered overnight to let the skin dry out.
Heat pan medium-high. Sear chicken skin-side down 6–7 minutes until golden and crisp, flip and cook 4 minutes. Set aside (chicken won't be fully cooked yet).
In same pan, sauté garlic, thyme, and chili flakes 30–45 seconds until fragrant.
Deglaze with chicken broth, scraping browned bits from the pan. Reduce slightly. Stir in heavy cream, butter, lemon juice, and Parmigiano. Simmer gently 2–3 minutes.
Return chicken to pan, cover, and simmer on low 8–10 minutes until chicken reaches 175°F.
Spoon sauce over chicken and garnish with parsley and extra Parmigiano Reggiano.
