Preheat the oven to 400°F (200°C).

In a large mixing bowl, combine the halved baby potatoes, minced garlic, olive oil, salt, pepper, and thyme. Toss until the potatoes are well coated.

Spread the potatoes in a single layer on a large baking sheet. Roast in the preheated oven for 15 minutes.

After 15 minutes, remove the baking sheet from the oven and add the trimmed asparagus. Toss everything together and return to the oven.

Roast for an additional 10-15 minutes, or until the potatoes are fork-tender and the asparagus is crisp-tender.

Remove from the oven and serve immediately, garnished with additional salt and pepper if desired.