Bring the water to a boil in a medium pot. Add 1 tsp (5 mL) salt and the broccoli. As soon as it turns bright green, remove it with tongs and cool under cold water. Drain in a sieve or colander and let sit while you prepare the other ingredients.
Add the quinoa to the pot the broccoli was dunked in. Keep at a lively simmer for 10 minutes. Drain the quinoa well, return it to the pot, and cover with tightly with a lid. Let sit for 20 minutes off the heat. Transfer the quinoa to a large bowl.
While the quinoa is cooking and resting, make the dressing. Whisk the lemon juice, vinegar, garlic, 1 tsp (5 mL) salt and pepper together. Slowly whisk in the olive oil. Toss with the quinoa and let cool.
Holding the broccoli by the stem, grate the florets and stalks using the large holes of a box grater. Toss the broccoli “dust” with the quinoa. Add the remaining ingredients and toss well. Taste and adjust the seasoning, and serve.
Note: Quinoa and grain salads will diminish in seasoning after refrigeration overnight. Check and correct the seasoning before serving.