Grilled Rib Eye with Paprika Vinaigrette
['1/2 cup vegetable oil', '2 tablespoons paprika', '1 large shallot, finely chopped', '1/3 cup coarsely chopped capers', '1/4 cup chopped fresh flat-leaf parsley', '2 tablespoons red wine vinegar', '1 tablespoon crushed red pepper flakes', 'Kosher salt', '2 32-ounce bone-in beef rib eyes (about 2" thick)', '2 tablespoons vegetable oil', 'Kosher salt', 'Freshly ground pepper', '2 tablespoons light brown sugar', '"2 tablespoons piment dEspelette or hot paprika"', 'Cheesecloth']
Heat oil and paprika in a small saucepan over medium heat, swirling pan occasionally, until warm, about 5 minutes. Remove from heat and let stand until oil is cool and turns dark red, 1–1 1/2 hours.
Strain paprika oil through a fine-mesh sieve lined with cheesecloth into a small bowl. Mix in shallot, capers, parsley, vinegar, and red pepper flakes; season with salt.
Let steaks stand at room temperature 1 hour before grilling.
Prepare grill for 2-zone heat (for a charcoal grill, bank coals on 1 side of grill; for a gas grill, leave 1 or 2 burners off).
Rub steaks with oil and season with salt and pepper. Cook steaks over direct heat, moving to a cooler area if flare-up occurs, until charred, about 4 minutes per side. Using tongs, hold steaks vertically to sear edges (bone side and fat-cap side) and render some fat, about 2 minutes per side. Grill steaks over indirect heat, turning occasionally, until an instant-read thermometer inserted into the center registers 125° for medium-rare. Transfer steaks to a cutting board and let rest 10-15 minutes. (Keep charcoal grill hot.)
Mix brown sugar and piment d'Espelette in a small bowl. Sprinkle over steaks and grill over direct heat until sugar is caramelized, about 1 minute per side. Transfer to a cutting board and slice. Serve with vinaigrette.
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