1. Preheat the oven to 425 degrees F. Trim any broccoli florets that are larger than 2 1/2-inches in diameter so all the pieces are all 2 to 2 1/2 inches in size (so they cook at the same rate). Toss the broccoli, edamame and carrots with 2 tablespoons of the Lemon Ginger Oil, 1 teaspoon salt and 1/4 teaspoon black pepper in a large bowl.
2. Spread an 18-inch-long piece of heavy-duty aluminum foil on a cutting board or work surface and spread the vegetables in the middle. Pour 2 tablespoons water over the vegetables and then bring two of the sides of foil up and together and fold over twice to seal. Bring the other two sides up and in, crimping to seal.
3. Put the foil packet on a rimmed baking sheet and bake 25 minutes. Carefully open the foil packet, as it will be very steamy, and toss the vegetables with any of the accumulated juices and oil in the bottom of the foil packet. The vegetables should be crisp tender with a few pieces a little more cooked, but if any vegetables seem raw, reseal the package and bake an additional 5 minutes.
4. Spoon the steamed vegetables and juices into a serving bowl. Sprinkle with the sesame seeds and sliced scallion. Drizzle with an extra tablespoon of the lemon ginger oil if desired.
Combine both of the oils, the lemon zest, garlic, ginger and red pepper flakes, if using, in a medium pot. Heat the mixture over medium-low heat until small bubbles form around the edges and the oil becomes fragrant, about 10 minutes.
Remove from the heat, cool completely and then strain, pressing on the solids to release all the flavored oil. You will not need all the oil for this recipe. Store the extra oil in a small jar or resealable plastic container in the refrigerator and use within one week. Before using, let stand at room temperature for at least 5 minutes.
From the Food Network Kitchens