Rinse your broccoli and cut off the bottom three inches of the thick stems. Use your knife to cut the broccoli into individual florets with 2-3 inches of stem on them. Thin the florets and stems by slicing them in half vertically, so they'll cook faster.
Place 3/4 cup of cold water in your largest skillet over high heat. Add your broccoli and spread it evenly in the pan, in a single layer if possible. Cover the skillet with a lid and cook the broccoli for 20 minutes, or until it is tender and just starting to brown. (The water will evaporate, and you'll be able to smell the broccoli starting to brown. You should be able to easily insert a fork into the broccoli when it's done. During cooking, flip over the broccoli once.)
While the broccoli is cooking, zest two lemons with a zester or box grater until you have a tablespoon of zest. (You want only the yellow part of the skin, not the white.) Rinse your parsley, remove the stems, and chop the leaves until you have two tablespoons of it. Peel and finely chop your garlic.
When the broccoli is cooked, turn off the heat and transfer the broccoli to a large serving bowl. Add two tablespoons of olive oil to your skillet and heat it on medium high. Add your garlic to the pan and cook it for 30 seconds or just a little longer to soften it, being careful that it doesn't burn. Turn off the heat and add the garlic and oil from the pan to your bowl of broccoli. Add the remaining two tablespoons of oil, the lemon zest, parsley, lemon juice and seasonings to the bowl and stir well with two spoons.
Let the broccoli sit at room temperature for 30 minutes to an hour to allow the flavors to meld before serving. Store leftovers in the refrigerator for up to five days.
It helps to weigh the broccoli in the store to start out with 1 1/4 pounds. Once you trim off the thick stems at home, you'll end up with a pound of broccoli to cook.