Preheat grill to medium-high heat, about 400°F (200°C) to 450°F (230°C).
Trim woody ends from asparagus spears. Wrap prosciutto around 1-2 spears of asparagus.
Brush bundles lightly with olive oil and season with everything seasoning.
Grill for 8-10 minutes, turning once halfway through, until prosciutto is crispy and asparagus is tender-crisp.
Remove from grill and serve immediately with lemon wedges.
Notes
Alternative oven method: Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper, then arrange the wrapped asparagus in a single layer. Bake for 12 to 15 minutes, or until the prosciutto is crispy.