Put the beets and 2 tablespoons of the oil in a bowl and toss to coat. Wrap the beets in aluminum foil and roast for about 30 minutes, or until tender when pierced with a fork. Unwrap the beets and set aside until cool enough to handle, then slip off their skins. Dice the beets into 1 inch cubes.
Whisk the remaining 2 tablespoons oil with the vinegar and shallot. Season with salt and pepper.
Core and julienne the Asian pear. Put the slices in a bowl of cold water mixed with a little lemon juice (acidulated water) to keep them from turning brown and crisp them a little. Drain the pear just before using.
In a large bowl, toss the arugula with the beets and Asian pear. Drizzle the vinaigrette over the salad, toss gently, and season with salt and pepper.