Preheat your oven to 220°C (430°F) and line a large baking sheet with parchment paper.
Cut the broccoli into evenly-sized florets and peel the carrots before slicing them into 1/4-inch sticks. This ensures they roast evenly and caramelize uniformly.
In a mixing bowl, toss the prepared vegetables with about 3 tablespoons of olive oil, making sure each piece is glossy and coated. Sprinkle with a pinch of flaky sea salt to enhance their natural sweetness.
Spread the vegetables out in a single layer on the prepared baking sheet, giving them enough space so they can brown properly. Pop the sheet into the oven and roast for 20 minutes, until the edges are deeply golden and fragrant.
After 20 minutes, check the vegetables. They should be starting to caramelize and develop crispy edges. At this point, sprinkle the minced garlic over the vegetables and toss gently to distribute. Continue roasting for another 5-7 minutes, until the garlic is fragrant but not burnt.
Once done, remove the baking sheet from the oven and transfer the vegetables to a serving dish. Squeeze fresh lemon juice or sprinkle lemon zest over the top for brightness, and finish with a light drizzle of olive oil and a pinch of flaky sea salt.
Serve immediately while hot and crispy, enjoying the smoky caramelized flavors with a fresh lemony finish.