Bring a large pot of water to a boil.  Pour the oil into a loaf pan or one quart casserole dish.  Add the garlic and 2 tablespoons of small leaves from the basil to the oil.  Wrap the remaining basil in a damp paper towel, cover, and refrigerate until time for serving.  Using a fine microplane grater, zest 1/2 of the lemon directly into the oil.  Using a vegetable peeler, strip two large pieces of the peel into the oil; make sure you have a little peel left on the lemon.  Drop the asparagus in the boiling water for 1 minute.  Using tongs, remove the asparagus from the water, tap the tongs on the side of the pot, shaking off any excess water, and lay the asparagus into the dish with the oil.   The asparagus should be completely submerged; add a little more oil if needed.  Wrap the pan with plastic wrap and refrigerate until thoroughly chilled, about 4 hours. 

Remove the asparagus from the oil and place in a single layer on a serving platter.  Sprinkle with salt and a tiny squeeze of lemon juice.  Grate or crumble the feta over the asparagus and garnish with a few basil leaves and a grate of lemon zest.