Take the filet mignon steaks out of the refrigerator and let them sit at room temperature for about 30 minutes. Preheat your oven to 400°F (200°C).

In a small bowl, mix together the crushed capers, dried oregano, salt, and black pepper. Rub the seasoning mixture onto both sides of the filet mignon steaks, ensuring they are well-coated.

Heat 1 tablespoon of olive oil in a large oven-safe skillet over medium-high heat. Once the oil is hot, carefully place the seasoned steaks into the skillet. Sear the steaks for about 3-4 minutes on each side, or until a nice brown crust forms.

Transfer the skillet to the preheated oven and roast the steaks for an additional 6-8 minutes for medium-rare, or until they reach your desired doneness. Remove the skillet from the oven and let the steaks rest for about 5 minutes before slicing.

In the same skillet, add the remaining tablespoon of olive oil over medium heat. Add the halved cherry tomatoes and minced garlic. Cook for 3-4 minutes, stirring occasionally, until the tomatoes are charred and softened.

Pour in the vegetable broth and balsamic vinegar, stirring to combine. Bring the mixture to a simmer and cook for another 5 minutes, allowing the flavors to meld and the sauce to slightly thicken.

Slice the rested filet mignon and arrange it on plates. Spoon the rich charred tomato gravy over the steaks and garnish with fresh basil.