Preheat your oven to 400 °F with the convection setting on (or 450 °F for traditional ovens).
Broccoli: Cut the step off of your broccoli and separate the florets. Cut about 1 inch off the bottom of the stem and then peel the tough skin. Cut the rest of the stem into even sized pieces. Submerge the broccoli in water for 3 minutes to remove excess dirt. Dry the broccoli in a salad spinner or with a towel.
Cauliflower: Cut your cauliflower in half and remove the stem from both sides. Separate the florets. If the florets are larger than 2-3 inches thick, I like to cut them in half so they roast at the same time as the other florets. Submerge cauliflower in water for 3 minutes to remove excess dirt and then dry with a salad spinner or a towel.
Transfer the cauliflower and broccoli onto the sheet pan. Pour the olive oil and mix both veggies with the tongs (or clean hands). Make sure all surfaces of the veggies are covered.
Sprinkle the garlic, salt, and black pepper on top. Mix again with the tongs (or clean hands).
Place in the middle rack of the oven for 10 minutes. Then flip the cauliflower and broccoli. Roast for another 5 minutes (or more) and check if the veggies are crisp with brown edges. Finished broccoli and cauliflower should be golden and have an al dente texture when you pierce it with a fork.
Transfer to a plate and sprinkle with lemon juice or parmesan cheese if you like. Serve immediately.