Caprese Chicken Lasagna

Name: Caprese Chicken Lasagna
Ingredients: 1 box lasagna noodles; 1 tbsp. extra-virgin olive oil; 2 lb. boneless skinless chicken breasts, cut into 1 pieces; 2 tsp. dried oregano; 0.25 c. balsamic vinegar; 4 large cloves garlic, minced, divided; 3 tbsp. butter; 3 tbsp. all-purpose flour; 2.5 c. milk; 5 c. shredded mozzarella, divided; 0.75 c. freshly grated Parmesan; 1 (16-oz.) container ricotta; 1 large egg; 6 roma tomatoes, thinly sliced; 0.5 c. thinly sliced basil leaves, plus more for garnish