Preheat your oven to 425°F and line a large baking sheet with parchment paper. While the oven heats, trim the green beans and leave them whole—this preserves their snap and texture when roasted. Peel the carrots and slice them into 2-inch sticks so they're roughly the same size as the green beans, ensuring even cooking throughout.

In a large bowl, combine the trimmed green beans and carrot sticks with the olive oil, honey, salt, pepper, and fresh rosemary. Toss everything together until the vegetables are evenly coated. Spread them in a single layer on your prepared baking sheet—avoid overcrowding, as this helps them roast rather than steam. Roast for 30-35 minutes, stirring halfway through, until the vegetables are tender and lightly caramelized at the edges. I like to give them a good stir at the midpoint to ensure even browning on all sides.

While the vegetables roast, melt the butter in a small pot over low heat. Add the freshly minced garlic and cook gently for 5-10 minutes, stirring occasionally, until the garlic turns golden brown and becomes fragrant. Watch carefully—low heat is key here to infuse the butter with garlic flavor without burning it. Once golden, remove from heat and stir in the lemon juice. For the best flavor, I always use fresh-minced garlic rather than pre-minced, as it creates a more vibrant, aromatic sauce.

When the roasted vegetables are tender and caramelized, transfer them to a serving dish or platter. Pour the warm garlic butter sauce over the top and toss gently to coat all the vegetables. The combination of the roasted vegetables with the fragrant garlic butter creates a rich, flavorful dish that's simple yet impressive.