Grilled Beef Filets with Caramelized Shallots

Position a rack in the center of an oven and preheat to 375°F.

In an ovenproof sauté pan over medium heat, melt the butter. Add the shallots and sauté, stirring occasionally, until tender and golden, 15 to 18 minutes. Add the broth, vinegar, cream, thyme, salt and pepper, stir to mix and bring to a simmer. Reduce the heat to medium-low and simmer until nearly all of the liquid has evaporated, 6 to 8 minutes more. Transfer the pan to the oven and bake until the shallots are browned and a crust has formed on the top, about 45 minutes.

Meanwhile, preheat a cast-iron grill pan over medium-high heat. Season the filets with salt and pepper and brush both sides with the oil. Grill the filets until charred and lightly springy when pressed with your finger, 3 to 4 minutes per side for rare to medium-rare, or until done to your liking. Let the filets rest about 5 minutes before serving and serve the shallots alongside.