Mix together the strawberries, brown sugar, and balsamic vinegar in a bowl. Allow to sit for 1 to 3 hours, stirring occasionally.

Preheat oven to 400°F (200°C).

Heat olive oil in an oven-safe skillet over high heat. Sprinkle filets with salt and pepper, then sear each side until well-browned, 1 to 2 minutes per side.

Slide the skillet into the oven and cook until the center is reddish-pink, about 10 minutes or until a thermometer inserted into the center reads 130°F (54°C). Rest steaks on a platter tented with foil.

Strain the strawberries and discard the liquid. Pour steak juices into a saucepan, add strawberries, and bring to a simmer over medium-low heat. Melt butter into the sauce, gently incorporating it by tilting the pan.