Rinse the fish. Rinse the fillets and pat dry with paper towels; set aside.
Season with the lemon garlic butter. In a mixing bowl, combine lemon juice, butter, garlic, Italian Seasoning, thyme, 1/2 teaspoon paprika, salt, and pepper. Rub the herb mixture over each fillet and set the fish aside.
Heat oil in a skillet. Over medium-high heat, heat 2 tablespoons olive oil in a large oven-safe skillet.
Sauté. Add the chopped onions to the skillet and cook over medium-high heat for 2 minutes; stir in the garlic and continue to cook for about 20 seconds, or until fragrant.
Add the rice. Stir in the rice, rosemary, and paprika; cook for 2 minutes, stirring frequently.
Pour in the broth. Add vegetable broth, milk, salt, and pepper; stir to combine. Bring the mixture to a boil; reduce the heat to low and cook for 4 minutes.
Add the fish over the rice. Arrange the prepared Tilapia over the rice, then continue cooking for 4 more minutes.
Bake. Remove from heat; cover with a lid and bake in the oven for 20 minutes. Remove the lid and continue to bake for 5 more minutes or until lightly browned on top.