Preheat the oven to 425°F. Line a 15x10-inch baking pan with parchment paper or a silicone baking mat and set aside.
In a small bowl, combine the minced garlic and ½ teaspoon of the kosher salt. Using the back of a spoon, press and mash the mixture until the garlic begins to release its oils and becomes fragrant. Let it rest for 5 to 10 minutes. Stir in the olive oil and set aside.
Trim the broccoli stems. Slice the stalks lengthwise into halves or quarters, depending on thickness. Place the broccoli on the prepared baking pan in a single layer.
Pour the garlic-infused olive oil over the broccoli. Add the olives and toss everything well to coat evenly. Sprinkle with the remaining ½ teaspoon kosher salt.
Roast for 20 to 25 minutes, tossing once or twice during cooking, until the broccoli is tender but still slightly firm in the center and deeply caramelized around the edges.
Transfer to a serving dish. Finish with a squeeze of fresh lemon juice, a sprinkle of flaky sea salt, and a light drizzle of olive oil if desired.
Notes
Dry the broccoli well after washing. Excess moisture prevents browning and the broccoli will steam instead of roast.• Do not overcrowd the pan. Spread the broccoli in a single layer so it caramelizes properly. Use two pans if necessary.• Cut the stems into similar-sized pieces so they cook evenly with the florets.• For extra flavor, add a pinch of red pepper flakes before roasting.• Leftovers can be reheated in a hot skillet or oven to bring back some of the crisp edges.