Preheat the broiler to high. Place the asparagus tips onto a rimmed baking sheet. Drizzle olive oil over the asparagus, sprinkle on the lemon zest, and season the tips generously with salt and pepper. Toss to coat. Broil the asparagus until tender-crisp and beginning to brown and sizzle, about 6-8 minutes, stirring once halfway through.
Meanwhile, rub the warm toast with the interior of the sliced garlic clove until fragrant. Butter each slice of toast. Place 4-5 asparagus tips on top of each slice. Gingerly nestle the soft boiled eggs on top of the asparagus. Season the eggs with more salt and pepper. Slice the eggs on one side with a sharp knife to allow the yolk to run. Serve promptly with lemon wedges.