Preheat your oven to 400°F. While it heats, scrub the potatoes under cold water and cut them into 1-inch cubes—keeping them uniform ensures even cooking. Peel the carrots and cut them into 1-inch thick rounds. Spread both vegetables on paper towels to dry them slightly; this helps them brown better during roasting. Lightly coat a large roasting pan (about 9x13 inches or similar) with cooking spray.

In a small bowl, combine the olive oil and butter together (the butter will soften from the warm oil). Mince the garlic finely and add it to the oil mixture along with salt, pepper, smoked paprika, and fresh thyme leaves. Stir everything together until well combined. This aromatic coating is where all the flavor comes from, so take a moment to make sure the seasonings are evenly distributed. I like to use freshly stripped thyme leaves rather than dried—the aroma makes such a difference in the final dish.

Add the prepared potatoes and carrots from Step 1 to the seasoning mixture from Step 2, then toss gently but thoroughly until every piece is evenly coated with the oil and butter mixture. Spread the vegetables in a single layer on your prepared pan, trying not to crowd them too much—if pieces are piled on top of each other, they'll steam instead of roast and won't develop that golden, caramelized exterior. A little space between pieces allows hot air to circulate and creates better browning.

Place the pan in the preheated 400°F oven and roast for 30-40 minutes, stirring halfway through cooking (around the 15-minute mark). This ensures even browning on all sides. The vegetables are done when the potatoes are fork-tender and the carrots are soft, and the edges should be golden brown and slightly caramelized. I always check a few pieces with a fork to make sure they're truly soft all the way through before pulling them out.

Remove the roasted vegetables from the oven and transfer them to a serving dish while still warm. Sprinkle the fresh parsley evenly over the top—the bright green color and fresh herbaceous flavor make a beautiful finish to the rustic, caramelized vegetables.