Wrap the beets in foil individually. Roast until the beets are tender, about 1 hour. Let cool.
Working over a bowl, segment the blood oranges: Cut away the peel and white pith using a sharp knife, leaving the blood orange flesh exposed, then gently cut between the membranes to release each orange segment into the bowl, catching the juices.
Peel the beets. Cut each beet in half lengthwise with a sharp knife. Cut each half lengthwise into 4 or 5 wedges and toss in a bowl along with the tarragon, shallot and half the orange juice.
Preheat the broiler on high. Cut four 1-inch-thick slices of bread. Brush each piece of bread with oil and sprinkle a pinch of salt and pepper on each side. Broil until golden, 2 minutes per side.
Spread cream cheese on one side of each slice of bread. Spoon the beet mixture evenly on top of the cream cheese. Top with blood orange segments, cherry tomatoes and a drizzle of olive oil, then garnish with extra tarragon. Sprinkle with salt to taste. Enjoy!