Combine 2 tablespoons brown sugar, the instant coffee, cocoa powder, mustard powder, chile powder, cinnamon and 1 teaspoon salt in a bowl; rub the mixture between your fingers until fine. Season the steak with salt, then generously rub with the coffee-spice mixture.
Heat the vegetable oil in a large cast-iron skillet over medium heat. Working in batches if necessary, sear the steak, 3 to 6 minutes per side for medium rare.
Transfer to a cutting board and let rest; reserve the juices in the skillet.
Add the remaining 1 teaspoon brown sugar and the onion to the skillet.
Sprinkle with 1/4 teaspoon salt, and pepper to taste; cook over medium-high heat, stirring frequently, until the onion is soft and golden, about 5 minutes.
Add the bell pepper and 1/4 cup water; cook, stirring, until crisp-tender, about 5 minutes. Stir in the lime juice. Season with salt and pepper.
Slice the steak against the grain. Divide the steak, bell pepper, onion and the juices from the skillet among plates.