Separate the broccoli into large florets and cut the stem in quarters lengthwise (or into big chunks); boil in salted water for 2-3 minutes, until it's bright green and just tender. Remove (with a slotted spoon, if you want to use your water to cook the grains) and set aside to cool, then roughly chop.
Heat a generous drizzle of oil in a large skillet set over medium-high heat, add the garlic and cook for a minute, then add the broccoli and cook, stirring and squeezing over some lemon and sprinkling with salt and pepper, for a few more minutes. Remove from the heat and toss with the grains and feta (cool the broccoli first, if you like), while you fry an egg or two in the pan. Serves 2-6.