Prepare the marinade by finely grating the zest of the lemons into a medium bowl. Juice the lemons and add the juice to the bowl.
Mince the shallot and garlic, then add them to the bowl with the lemon zest and juice.
Pour in the olive oil and add dried oregano, kosher salt, paprika, and black pepper. Whisk the mixture until fully combined.
Pat the chicken thighs dry with paper towels. Add the chicken to the marinade and turn to coat evenly.
Cover and refrigerate for at least 1 hour or up to 2 hours to allow the flavors to soak into the chicken.
Meanwhile, remove the leaves from the parsley sprigs and finely chop them. Refrigerate until ready to use.
Heat a large skillet over medium-high heat until hot.
Add half of the marinated chicken in a single layer, shaking off excess marinade back into the bowl. Cook for 5 to 6 minutes per side until browned and the internal temperature reaches 165°F.
Transfer the cooked chicken to a serving plate.
Remove any remaining garlic pieces from the pan and repeat cooking with the remaining chicken.
Sprinkle chopped parsley over the chicken before serving.