Heat oven to 450 degrees. Place beets in an 8-by-8-inch baking pan coated with olive-oil cooking spray; cover with foil. Place in oven; roast until tender, 45 to 55 minutes, depending on size. Allow beets to cool, remove skins, and cut into 3/4-inch chunks, reserving half a peeled beet for vinaigrette.
Using a paring knife, remove peel, pith, and outer membranes from the oranges. Carefully cut each segment away from membranes, collecting juice and segments in a bowl. Squeeze any remaining juice from membranes before discarding. Drain segments, and set aside, reserving 1/4 cup juice.
Place reserved half beet, reserved orange juice, red-wine vinegar, salt, and pepper in a blender; puree until smooth. With motor running, add canola oil, and process until combined. Stir in 2 tablespoons chopped parsley.
Place lettuce, endive, reserved beets, oranges, and remaining parsley in a bowl. Just before serving, add vinaigrette, and toss. Garnish with ricotta salata, and serve.