Put the sliced garlic in a bowl, season with coarse salt and work the salt into the garlic using your fingers. Let sit for at least 10 minutes.
Bring a large pot of water to a boil, add the asparagus and cook for 2 minutes. Drain and plunge into a bowl of cold water to stop the cooking.
Drain and dry the asparagus spears, then cut thinly on the bias. Arrange the asparagus on a plate, and sprinkle the garlic on top. Drizzle some oil over the top.
Using a vegetable peeler, scrape away about 1 inch of the horseradish skin from the end of the root; give it a rinse. Grate the root over the asparagus.
Season with more salt, if needed, and serve with lemon wedges.
1 or 2 heads green garlic, finely sliced
Coarse sea salt
1 bunch asparagus, trimmed and washed
1 tsp freshly grated horseradish root
1 tbs olive oil
Half a lemon