Preheat the oven to 475 degrees F.

Cut the backbone out of the squab and gently flatten with the palm of your hand. Lightly season the squab on both sides with salt and ground black pepper.

Heat the oil in a large saute pan or skillet over medium-high heat. Add the squab, skin-side down, and cook for 3 minutes. Turn and place in the oven. Roast until the birds are cooked through and tender, about 7 minutes. Remove from the oven and transfer to a platter. Cover with aluminum foil. Drain all but 1 tablespoon of fat from the pan and place over medium-high heat. Add the shallots to the pan and cook, stirring, for 1 minute. Add the garlic and cook for 30 seconds. Add the cherries and cook, stirring, for 1 minute. Add the balsamic vinegar and cook, stirring, to deglaze the pan. When nearly all the vinegar has evaporated, add the chicken stock and sage. Cook until reduced by 25 percent in volume, about 1 1/2 to 2 minutes. Remove the sauce from the heat, add the butter and stir. Adjust the seasoning, to taste.

For the Fried Nests: Preheat a fryer to 360 degrees F.

Dredge the beets and sweet potatoes in the flour, shaking off any excess. Place the sweet potatoes and beets in the fryer and cook until golden brown, about 4 to 5 minutes. Remove the beets/sweet potatoes from the fryer with a spider to a paper towel lined plate and season with salt.

To serve, place the potato nest on a platter. Place squab on top and top with sauce. Arrange the haricots verts around the sides and serve immediately.

Bring a small saucepan of salted water to a boil. Add the haricots verts and cook until just tender, about 1 minute. Transfer with a slotted spoon to an ice bath to refresh. Drain. In a large skillet, melt the butter over medium-high heat. Add the drained haricots verts, and cook, stirring, for 3 minutes.