1. Heat the oven to 450°. In a small bowl, combine the mayonnaise, garlic, 2 tablespoons of the oil, the lemon juice, cayenne, and a pinch of salt. Mix well and refrigerate until ready to use.
2. Put the potatoes and carrots on a large baking sheet and toss them with 2 tablespoons of the oil and 1/2 teaspoon salt. Spread the vegetables out in a single layer and roast them in the oven for 15 minutes.
3. Meanwhile, put the bell-pepper strips on a second large baking sheet and toss them with 1 teaspoon of the oil and 1/8 teaspoon salt. After 15 minutes, take the first pan out of the oven and turn the vegetables with a spatula. Put both pans in the oven and roast for 5 minutes. Toss the asparagus with the remaining 2 teaspoons of oil and 1/8 teaspoon salt. Put the asparagus on the pan with the peppers. Roast until all the vegetables are tender, about 10 minutes longer. Serve the roasted vegetables and hard-cooked eggs with the aioli.
Plenty of other vegetables lend themselves to roasting. Try wedges of sweet potato or fennel, whole scallions or mushrooms, or halved Brussels sprouts.
Wine Recommendation: Roasted vegetables and pungent aioli are best partnered with a fairly neutral-flavored, high-acid wine with some body. Italy's Collio region produces delicious pinot grigios that perfectly match that description.