Coffee-Rubbed Steak With Peppers and Onions

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2 tablespoons plus 1 teaspoon packed light or dark brown sugar

1 tablespoon instant coffee

1 teaspoon unsweetened cocoa powder

1 teaspoon mustard powder

1/2 teaspoon ancho chile powder

1/8 teaspoon ground cinnamon

Kosher salt

1 1 1/4-to-1 1/2-pound skirt steak, cut into 4 pieces

2 teaspoons vegetable oil

1 large onion, cut into wedges

Freshly ground pepper

1 green bell pepper, cut into strips

Juice of 1/2 lime, plus lime wedges for serving

Cornbread, for serving (optional)