Thoroughly wash 1 tablespoon of fresh rosemary under cool, running, drinkable water. Mince the rosemary.
In a medium bowl, add the minced rosemary, ¼ cup of grated Parmigiano-Reggiano, 1 teaspoon of ground sage, 1 teaspoon of kosher salt and 1 teaspoon of freshly ground black pepper. Mix until combined.
Drizzle 5 skin-on bone-in chicken thighs with extra-virgin olive oil and coat the chicken skin with the Parmesan mixture, repeat on all pieces and set aside.
Thoroughly wash 1 lemon (including the rind) under cool, running, drinkable water.
In a medium bowl, zest and juice the whole lemon along with 1 cup chicken broth. Mix and set aside.
In a large non-stick oven-safe sauté pan on medium heat, add 1 tablespoon of unsalted butter and 1 tablespoon of extra-virgin olive oil. Place the chicken skin-side down and sauté until golden brown and crisp, about 4 minutes. Flip chicken and cook for an additional 3 minutes.
Add lemony broth mixture to the pan and bake for 10-15 minutes until the chicken registers 165°F on an instant-read thermometer. Eat up, Mama!
Tip: Stockpile (pun intended!) the leftover bones in an airtight plastic bag and store in the freezer to make broth at a later date.