Wash and scrub the beets, and then season them with a pinch of salt.
Wrap the beets in aluminum foil, place them on a baking sheet, and bake them until fork tender, about 1 hour. Allow them to cool to the touch, peel them with a towel or paring knife, cut them into quarters, and set them aside.
In the meantime, carefully shave the radishes and carrots with a mandoline into a bowl of ice water and set them aside to get crispy until you need them.
To make the vinaigrette: In a blender, combine the pear, Dijon mustard, garlic, olive oil, shallot, and cider vinegar and purée until fully emulsified and smooth.
Season the vinaigrette with salt and pepper. Set aside.
To compose the salad: Drain the radishes and carrots, and pat them dry with a paper towel.
In a large salad bowl, combine the beets, radishes, carrots, tart cherries, radicchio, parsley, and basil.
Using a veggie peeler, shave the Manchego cheese over the salad.
Drizzle 3 tablespoons of the vinaigrette over the salad. Serve the extra vinaigrette on the side.