Wash the broccoli thoroughly under running water. Cut it into small florets and cut the stems into similar-sized pieces. Remove any tough outer skin from the stems if present.
Place the broccoli in a deep pot on the stove. Cover it with water and add 1 teaspoon of salt.
Let the broccoli boil over high heat. Once boiling, reduce the heat and let it cook for an additional 4 minutes. Then, drain the water.
Heat the olive oil in a pan over the stove. Add the minced garlic and sauté until fragrant.
Add the boiled broccoli to the garlic mixture and stir for about 4 minutes.
Add the lemon juice, black pepper, and the remaining teaspoon of salt. Stir to combine.
Transfer the sautéed broccoli to a serving plate and serve immediately.