Pat the chicken dry. Use paper towels to remove surface moisture on the thighs. Dry skin equals better browning and crispier texture.
Season both sides with 1 teaspoon salt, pepper, and paprika if using.
Brown the chicken. Heat olive oil in a large skillet over medium heat. Add chicken skin-side down and cook undisturbed for 8–10 minutes, until the skin is deeply golden and crisp. Flip and cook 3–4 minutes more.
Transfer to a plate; keep the fat in the pan.
Sweat the aromatics. Lower heat to medium-low. Add butter, garlic, and shallot. Cook 3–4 minutes, stirring, until the garlic is fragrant and lightly golden at the edges.
Don’t let it burn.
Deglaze. Pour in white wine, scraping up browned bits. Simmer 2–3 minutes until slightly reduced. Add chicken broth and thyme; bring to a gentle simmer.
Make it creamy. Stir in cream and Dijon.
Simmer 2 minutes until the sauce thickens slightly. Taste and add the remaining ½ teaspoon salt if needed.
Return the chicken. Nestle thighs skin-side up into the sauce. Reduce heat to low, cover loosely, and cook 8–12 minutes, until the chicken reaches 165°F in the thickest part.
Brighten. Stir in lemon zest and juice.
This wakes up the richness and keeps the sauce from feeling heavy.
Rest and garnish. Let the chicken sit off the heat for 3 minutes to settle. Sprinkle with parsley. Spoon sauce over the thighs when serving.