Preheat oven to 375 degrees and place oven rack in the center of oven.
Heat 2 tablespoons of olive oil in a large dutch oven or 3.5 quart braised on medium heat.
Season lamb shanks with 1 teaspoon herbs de Provence, 1 teaspoon kosher salt, and ½ teaspoon ground black pepper. Sear the shanks on all sides—about 3 minutes on each side. Remove shanks to a plate.
Next, add the carrots, shallots, celery, and garlic to the pot and cook, stirring occasionally, until vegetables are translucent, about 5 minutes. Add the tomato paste and stir until the vegetables are evenly coated in the tomato paste.
Add in your red wine and begin to deglaze the pot, using a wooden spoon to scrape up the brown bits that have collected at the bottom of the pot. Next, add in the chicken stock followed by the bay leaf, thyme/rosemary bunch, and crushed red pepper flakes (if using).
Allow braising liquid to come to a slow simmer before adding the lamb shanks back to the pot. Place dutch oven into the preheated oven and roast for 1 hour and 30 minutes, until the shanks are fork tender and meat starts to fall off the bone. Internal temperature should register between 145 and 150 degrees Fahrenheit.
Serve with mashed potatoes or herby polenta and roasted or sautéed seasonal veggies.