In a small bowl, combine kosher salt, black pepper, smoked paprika, garlic powder, dried thyme, onion powder, and cayenne pepper.
Pat the chicken leg quarters dry with paper towels. Rub the spice mixture evenly over all sides of the chicken quarters.
Heat olive oil in a large skillet over medium-high heat. Add the chicken quarters skin-side down and sear for 3-4 minutes until the skin is golden brown. Flip and sear the other side for 2 minutes. Remove from heat.
Place the sliced onion and minced garlic in the bottom of the slow cooker.
Arrange the seared chicken quarters on top of the onions and garlic in the slow cooker.
Pour the chicken broth and lemon juice over the chicken.
Add the fresh rosemary sprigs on top of the chicken.
Cover and cook on low for 6 to 7 hours, or until the chicken is tender and reaches an internal temperature of 165°F (74°C).
Remove the rosemary sprigs before serving. Serve the chicken quarters hot with the cooked onions and pan juices spooned over.