Heat the oil in a medium skillet over medium heat. Add the onion and cook until softened, 3 to 5 minutes. Add the mustard, honey, vinegar, red pepper, ½ teaspoon salt, and ¼ teaspoon black pepper and bring to a simmer. Cook, stirring often, until slightly thickened, 4 to 6 minutes.
Reserve half the sauce for dipping, if desired. Cook 1½ to 2 pounds of beef, pork, poultry, lamb, seafood, or tofu on a preheated grill to desired doneness. Brush on the sauce during the last 2 to 3 minutes of cooking.