Preheat your grill or grill pan. Heat to medium-high. You want it hot enough to char the vegetables quickly without burning them.
Prep the vegetables. Rinse the asparagus and flower sprouts.
Pat dry very well. Trim the woody ends of the asparagus. If any flower sprout leaves are tough or wilted, peel them away.
Season. In a large bowl, toss asparagus and flower sprouts with olive oil, lemon zest, lemon juice, smoked paprika (if using), salt, black pepper, and red pepper flakes.
Make sure everything is lightly coated.
Make the vegan aioli. In a small bowl, whisk vegan mayonnaise, garlic, Dijon, lemon juice, olive oil, salt, and pepper until smooth. Taste and adjust lemon and salt. If you like it thinner, whisk in a teaspoon of water.
Grill the asparagus. Place asparagus perpendicular to the grates.
Grill 3–5 minutes, turning once or twice, until crisp-tender with light char. Thinner spears cook faster; thicker ones need another minute.
Grill the flower sprouts. Arrange the sprouts cut-side down if they’re halved, or in a grill basket if you have one. Grill 4–6 minutes, tossing occasionally, until edges are charred and centers are tender but still have bite.
Finish and season. Transfer vegetables to a platter.
Sprinkle a pinch more salt and an extra squeeze of lemon juice over the top while hot to brighten the flavors.
Serve with aioli. Spoon the vegan aioli over the vegetables or serve on the side for dipping. Add nuts and herbs if you like, and pass lemon wedges at the table.