Preheat the oven to 400 F.
Peel the beets, then place in a loaf pan and drizzle with a couple of teaspoons of the oil. Cover with foil, then roast for 40-60 minutes, until tender when pierced with a knife. Let cool completely.
In a cup, stir the remaining oil, balsamic, salt and pepper.
Slice the cooled beets. Use a channel knife to cut grooves along the cucumber, if desired, then slice. Halve the tomatoes. Toast the hazelnuts for 10 minutes, rub off the skins with a towel, then chop coarsely.
Spread the greens on a plarge platter, then arrange the beet slices on top. Arrange cucumbers on top, then place tomato halves around the plate. Drizzle with dressing. Sprinkle with hazelnuts, then serve.