Start by getting a big kettle of pasta water going; salt it when it gets hot. Do this before you start picking off all the tender agretti leaves. Generally everything is good to eat except for the central woody stem.
Drop the angel hair into the boiling water and separate it; angel hair has a tendency to stick to itself. It will need about 5 minutes to cook.
As soon as you drop the pasta in, heat the olive oil in a large saute pan over medium-high heat. Add the anchovy fillets and mash them up well in the oil; doing this makes the dish more savory, and not fishy. Let this cook for a minute or two, then add the garlic. Let that cook for about 1 minute, then add the agretti and cayenne. Stir and cook until the agretti wilts.
When the angel hair is done, move it directly to the pan; you want some of the pasta water to get into the pan. Mix and stir this well, adding the cheese, black pepper and lemon to taste. Serve at once, maybe with a bit more olive oil drizzled over it.