Set a skillet over medium heat; heat up 1 tablespoon olive oil and 1 tablespoon butter.
Season the fish with salt and pepper and transfer it to the skillet; cook for 3 minutes per side. Remove the fish from the skillet and set aside.
Add 1 tablespoon butter to the same skillet and melt over medium-high heat. Stir in the garlic and cook for 15 seconds.
Slowly whisk in the chicken broth and cook for 4 minutes or until reduced by 1/3. Reduce heat to medium-low and add remaining butter. Slowly whisk in the heavy cream.
Add lemon juice and whisk until everything is well combined. Make sure to whisk continually so that the heavy cream doesn't curdle.
Season with salt and pepper, then taste the sauce and adjust accordingly.
Remove from heat.
Pour the sauce over the fish, or return the fish back into the skillet and spoon the sauce over it.
Garnish with parsley and serve.
Notes
Choose freshtilapia fillets that are firm, have a translucent color, and do not have a fishy odor. Thaw the filets if they are frozen.
Preheat your skillet so it is well-heated before cooking the fish to achieve a perfect sear that locks in flavors.
Keep stirring the sauce to ensure the cream and lemon integrate perfectly without curdling.
Serve the tilapia with a side of steamed vegetables, mashed potatoes, or a fresh salad to complete the meal.