Preheat the grill to medium-high and soak skewers for 10 minutes.
Make the relish: In a medium mixing bowl, whisk together mustard, olive oil, red wine vinegar, salt, and pepper, mix in 1/2 cup chopped red onion and parsley. Set aside.
On a rimmed sheet pan drizzle olive oil over beef, broccoli, peppers, and remaining red onion, chopped into 1" cubes, toss until well coated and season generously with salt and pepper. Skewer meat and vegetables alternately.
Place skewers on grill and cook, rotating as needed until meat and vegetables are browned, 5 minutes or until desired doneness. Transfer skewers to a large platter and serve with Dijon-onion relish.
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