For appetizers, heat oil in a small pot with garlic until it bubbles, simmer a minute. Brush a skillet with garlic oil and heat over medium-high heat. Add the first tortilla and blister it 30 seconds, flip and cover half of the surface with arranged layers of mozzarella, basil and tomatoes, season with salt and pepper and fold over the quesadilla, cook 30 seconds on each side to set. Remove from pan and repeat. In less than 10 minutes, you'll have 4 half moons (mezza lunas). Cut into quarters and serve.
Pour a couple tablespoons of remaining oil into a skillet over medium-high heat. Season the chicken with salt and pepper. Cook chicken 6 minutes on each side, turning once, until golden and juices run clear. While chicken cooks, heat 1-inch water over high heat in small high sides skillet, to a boil. Add salt and broccolini to the water and cook 3 to 4 minutes, drain and reserve. Meanwhile, heat 2 tablespoons butter over medium heat in a small sauce pot, stir flour into melted butter, cook 1 minute then whisk in milk and cook to thicken, about 2 to 3 minutes, stir in cheese and season with salt and pepper. Serve chicken topped with broccolini and pour sauce over top - in less than 15 minutes you have a low maintenance Chicken Divan!