Remove filet mignon from refrigerator 20–30 minutes before cooking. Pat dry and season both sides with salt and black pepper.
Heat olive oil in a heavy skillet over medium-high heat until hot.
Sear steaks for 3–4 minutes per side until a golden crust forms.
Add 2 tbsp butter and smashed garlic to the pan. Baste steaks with melted butter for 1–2 minutes.
Cook to desired doneness (130–135°F for medium-rare). Remove steaks and let rest for 5 minutes.
In the same pan, add red grape juice, beef broth, thyme, and balsamic vinegar. Simmer for 4–5 minutes until slightly reduced.
For a thicker sauce, stir cornstarch with 1 tbsp water and add to the pan, simmering briefly until thickened.
Remove from heat and whisk in 1 tbsp cold butter for a glossy finish.
Spoon sauce over rested filet mignon and serve immediately.