Heat olive oil, salt, and black pepper in a skillet over medium heat. Cook scallops in hot oil just until opaque in the center, about 3 minutes.
Combine chicken broth, wine, and lemon juice in a saucepan. Bring to a boil; cook until reduced by half, about 5 minutes. Add garlic, butter, and capers; simmer until garlic sauce is fragrant, about 2 minutes.
Pour garlic sauce over scallops in the skillet. Add broccoli. Reduce heat to medium-low, cover, and let steam until broccoli softens, about 7 minutes.
Bring 2 cups of water to boil in a saucepan. Add ramen noodles and cook until soft, about 3 minutes. Drain noodles; stir into scallops. Add cornstarch, mixing well to make sure there are no lumps.
Remove skillet from heat, cover, and let sit until flavors combine, about 2 minutes.