Preheat the oven to 425 degrees . Place the garlic cloves on a piece of foil and drizzle with 1 tablespoon EVOO. Enclose the garlic in the foil and roast until soft and just golden, about 25 minutes.
Meanwhile, in a large pot of boiling, salted water, cook the asparagus until crisp-tender, about 2 minutes. Remove with a strainer and refresh in cold water; drain. Add the pasta to the pot and cook until al dente; drain, reserving 1/2 cup of the pasta cooking water. Reserve the pot.
Using a blender, puree the roasted garlic, the vinegar, lemon juice and sugar. With the machine on, slowly add 1/4 cup EVOO.
In the reserved pot, heat the remaining 1 tablespoon EVOO over medium-high heat. Add the onion and cook until softened, about 5 minutes. Add the pasta, asparagus, roasted garlic vinaigrette and the reserved pasta cooking water; toss to combine and season with salt and pepper.