Rinse the broccoli and cauliflower under cool water and dry thoroughly with paper towels.
Cut the vegetables into large florets and place in a large bowl. Smaller florets tend to get tough and chewy when roasting.
In a small bowl, whisk together the olive oil, lemon juice, garlic, and Dijon mustard. Pour the mixture over the veggies and toss gently with a rubber spatula (or your hands) until all the vegetables are evenly coated.
Pour the vegetables onto a parchment paper or aluminum foil lined rimmed baking sheet (or on a rimmed baking stone). Spread into an even layer, making sure the veggies are not crowded, otherwise they will steam instead of roast.
Sprinkle evenly with the salt and freshly ground black pepper. Bake for 20 minutes, stirring halfway through, until tender and slightly caramelized or golden brown on the edges.
Remove the pan from the oven and give the veggies a squeeze of lemon juice, if you like.
If necessary, use more than one baking sheet to be sure the vegetables have plenty of room.