Bring a large pot of generously salted water to a boil over high heat.
Meanwhile, tear off any broccoli leaves and trim the bottoms of the stems. Cut the florets just above where they join the large stem, and then cut each floret lengthwise in half or in quarters through its stem (but not the buds). The top of each floret should be about the size of a quarter. Using a vegetable peeler or paring knife, peel the tough outer skin from the large stem, removing as little flesh as possible. Cut the stem into baton-shaped pieces about 1/4 inch wide and 2 inches long.
Boil the florets and stem pieces until they’re tender (pierce with a paring knife or taste a piece) but still offer a bit of resistance, about 3 min. Drain the broccoli, spread it on a baking sheet in an even layer, and set aside to cool—it will continue to cook as it cools.
Put the currants in a small bowl, add enough hot water to cover, and let sit until softened, about 10 min. Meanwhile, using a mortar and pestle or the flat side of a chef’s knife, mash the garlic to a paste with a pinch of salt. Transfer the garlic to a small bowl and add the vinegar and cayenne. Let sit for about 10 minutes.
Warm 1 Tbs. of the oil in a small sauté pan over medium heat. Add the slivered almonds and fry, stirring frequently, until golden brown, 2 to 3 min. Transfer to a plate lined with paper towels and season with salt.
Drain the currants. Whisk the remaining 4 Tbs. oil into the vinegar mixture. Just before serving, combine the broccoli, currants, feta, and half of the almonds in a large bowl. Drizzle with the vinaigrette and toss gently to combine. Taste and season with a pinch more salt if necessary. Transfer to a serving platter and sprinkle with the remaining almonds and the cilantro, if using.