Slice the red onion into ¼-inch rings. If you have time to fire up your grill, the smoky, grilled red onions really bring thise benedict to the next level. Coat the onion rings with oil and sprinkle with salt and pepper. Grill on a medium-high heat for 4 to 5 minutes on each side, until softened and lightly charred.
If you’re not grilling, heat a large skillet over medium-high heat and add 2 to 3 teaspoons of cooking oil. Sauté the red onion rings with a big pinch of salt until softened and starting to brown in spots, 5 to 7 minutes. Remove from the heat and set aside.