Pour 3 tablespoons olive oil into a shallow platter and lay chicken breasts on top. Rub with lemon juice, salt and pepper.
Heat 2 tablespoons olive oil in a nonstick skillet over medium-high heat and cook chicken breasts until browned, about 4 minutes per side.
Preheat oven to 350 degrees F (175 degrees C). Grease a baking dish. Place tomatoes and green onions in the baking dish and pour chicken broth on top.
Combine mustard, rosemary, and thyme in a small bowl and brush onto chicken breasts. Place chicken breasts on top of the vegetables in the baking dish. Cover with Gruyere cheese.
Bake in the preheated oven on the middle rack until chicken is no longer pink in the center and the juices run clear, about 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).