2 tsp fresh lemon juice
2 tsp Sherry wine vinegar
1-1/2 tsp finely grated lime peel
1 cup mayonnaise
1 tsp piment d'Espelette
Coarse sea salt
Freshly ground black pepper
Vegetables: any combination of zucchini, summer squash, mushrooms, bell pepper, red or white onions, eggplant, asparagus, trimmed and sliced for the grill
Combine shallot, lemon juice, vinegar, and lime peel in medium bowl. Cover; let stand 30 minutes. Whisk in mayonnaise and piment d'Espelette. Season with salt and pepper. Cover; chill 2 hours.
Meanwhile, heat your grill (or broiler, if you're cooking inside). Brush the vegetables on both sides with a few teaspoons of olive oil, and sprinkle with sea salt and black pepper. Cook on the grill (or in the broiler) for 2-3 minutes per side, until the vegetables are just cooked through but still crunchy.
Arrange vegetables on a platter and let cool for at least 15 minutes. Top with piment d'Espelette sauce, and serve at room temperature or cold.