Heat the butter and 2 tablespoons of the oil in a large skillet over medium-high heat.
Add the broccoli and cauliflower in a single layer, sprinkle with 1/2 teaspoon salt and cook, undisturbed, until the undersides are browned in spots, 3 to 4 minutes. Continue to cook, stirring every 1 to 2 minutes, until browned all over and crispy and tender, about 5 minutes more.
Reduce the heat to medium and push the vegetables to one side of the skillet. Add the garlic and remaining 1 tablespoon oil to the empty side and cook, stirring, about 30 seconds. Mix the garlic into the vegetables and add a large splash (about 3 tablespoons) of water. Squeeze in half a lemon, if using. Cook, stirring, until the juices have evaporated.