Heat 2 tablespoons oil in a small saucepan overmedium-high heat.
Add onion, garlic, andchile; season with salt and pepper. Cook,stirring often, until soft, about 5 minutes.
Add tomato paste to saucepan andcook, stirring, until beginning to darken,about 1 minute. Stir in Worcestershiresauce, vinegar, brown sugar, mustard, andhot sauce; simmer until slightly thickened,about 5 minutes.
Transfer to a blenderand purée with 1/2 cup water until smooth.Strain through a fine-mesh sieve intoa small bowl, if desired. Set sauce aside.
Heat remaining 1 tablespoon oil in a largeskillet over medium-high heat. Seasonsteak with salt and pepper and cook,turning occasionally, until deeply brownedand an instant-read thermometer registers130°F for medium-rare, 8–10 minutes.
Transfer meat to a cutting board; let rest5 minutes before slicing.
Serve with sauce.
DO AHEAD: Steak sauce canbe made 1 week ahead. Cover and chill.