Preheat oven to 425. Very thinly slice half of lemon, discard seeds. Cut remaining half into 2 wedges.
Season chicken thighs with salt and pepper.
Coat a large room temperature skillet with 1 tsp oil. Add chicken (skin side down if you are lucky enough to find skin on thighs, letting fat render and brown until chicken is cooked halfway through, about 10 minutes.
Scatter half the lemon slices on top of chicken and half in bottom of skillet. Transfer skillet to oven leaving skin side down Roast utnil chicken is cooked through skin is crisp and lemonslices on bottom are caramelized 6-8 minutes.
Transfer chicken and the caramelized slices from the bottom of skillet to warm platter. Leave softened lemon slices from top in skillet. Return skillet to medium heat. Add oregano, shallot, garlic and red pepper flakes, cook stirring frequently until fragrant about 1 minute. Remove from heat.
Add wine, cook over medium heat until reduced by half, 1 to 2 minutes.
Add broth, cook until thickened about 3 minutes. Squeeze 1 lemon wedge over and season sauce with salt pepper and juice from remaining lemon if desired. Drissle with 2 tsp oil.
Return chicken to skillet, skin side up to rewarm, serve topped with caremalized lemon slices.