How to Make It
On a large baking sheet, brush the rib-eye steaks on both sides with 2 tablespoons of the olive oil and season with 1/2 tablespoon each of salt and coarsely ground pepper. Let the steaks stand at room temperature for 2 hours.
Meanwhile, preheat the oven to 350°. Working in batches, pulse the focaccia in a food processor until it is chopped into coarse crumbs. Transfer the crumbs to a large bowl and toss with 2 tablespoons of the extra-virgin olive oil. Spread the bread crumbs on a large rimmed baking sheet and bake them for about 30 minutes, turning and stirring occasionally, until the crumbs are dry and golden. Let cool.
In a large bowl, mix the shallots with the vinegar and let stand for 15 minutes. Add the capers and thyme, then slowly whisk in the remaining 1/2 cup of olive oil until blended. Add the bread crumbs, season with salt and pepper and toss well.
Light a grill or preheat a cast-iron grill pan. Lightly brush the grate or grill pan with vegetable oil. Grill the steaks over a medium-hot fire until deeply browned on both sides, about 6 minutes for medium rare. Transfer the steaks to a cutting board and let rest for 10 minutes. Thickly slice the steaks across the grain and arrange on a platter. Spoon half of the bread-crumb salsa over the meat and pass the rest at the table.