In a large bowl, toss the potatoes with 1 Tbsp of olive oil until well coated. Add in the rosemary, salt, 1 1/2 tsp of the garlic, thyme and paprika and toss to coat.
Place onto a large baking sheet, cut-side down, and cover with tinfoil. Bake for 15 minutes.
While the potatoes cook, toss the asparagus with 2 tsp of olive oil and the rest of the garlic.
Once 15 minutes is up, spread the asparagus onto the pan. Additionally, drizzle the potatoes with the remaining oil and toss with a fork to coat.
Cover the pan and bake another 10 minutes. Then, uncover the pan and bake for 10-15 minutes, until the potatoes are soft and golden brown.