Trim the woody ends from the asparagus by snapping or cutting off about 1-2 inches from the bottom of each spear—they'll naturally break at the tender point if you bend them gently. Rinse the trimmed asparagus and pat completely dry with paper towels, as moisture will prevent proper browning on the grill. While preparing the asparagus, preheat your grill to medium heat (around 400-425°F) so it's ready when you need it.
In a small bowl, whisk together the olive oil, balsamic vinegar, minced garlic, fresh thyme, salt, pepper, and Dijon mustard until well combined. The mustard acts as an emulsifier, helping the oil and vinegar stay together and adding subtle depth to the marinade. Taste the mixture and adjust seasoning if needed—I like to add just a touch extra salt since it brings out the balsamic's natural sweetness.
Place the dried asparagus on a large plate or baking sheet and drizzle with about two-thirds of the balsamic marinade from Step 2, tossing gently with your hands or tongs to coat evenly. Lay the asparagus perpendicular to the grill grates (so they don't fall through) and grill for 8-12 minutes depending on thickness, turning every 2-3 minutes to develop an even char and ensure tender, evenly cooked spears. The asparagus is done when the tips are slightly caramelized and the stalks are tender when pierced with a fork but still have a bit of bite.
Transfer the grilled asparagus back to a serving bowl or platter and drizzle with the remaining marinade from Step 2, tossing gently to coat. Serve immediately while warm so the asparagus retains its tender-crisp texture and the residual heat allows the balsamic glaze to coat each spear beautifully. I find that serving it right away ensures the best flavor and prevents the asparagus from becoming too soft.