In a medium bowl, whisk together flour, baking powder, sugar, and salt. Add cold butter and shortening. With your fingers, quickly break up the fat into the dry ingredients. Rub the fats into the dry ingredients until well incorporated. Some butter pieces will be the size of small peas, other will be the size of oat flakes. Toss in blue cheese crumbles. Stir to incorporate.
Create a small well in the center of the flour mixture. Add buttermilk all at once. With a fork, quickly bring together the wet and dry ingredients. The dough will be rather shaggy. Dump dough out onto a lightly floured work surface. Knead dough about 10 times, bringing it together into a disk. Wrap dough in plastic wrap and refrigerate until the filling is assembled.
Add olive oil and butter to a medium saute pan over medium heat. Add sliced onions and season with salt and pepper. Cook and brown onions, stirring occasionally, until caramelized, about 18 to 20 minutes. Add garlic and cook for one minute more. Remove pan from heat, add balsamic vinegar and set aside.
In a large bowl, toss together clean cherry tomatoes (no need to cut them), chopped basil, flour, and red pepper flakes. Add caramelized onions and toss together until everything is lightly and evenly coated in flour. Season with salt and pepper
Place rack in the upper third of the oven and preheat oven to 375 degrees F.
Pour the tomato and onion filling into a square 8×8-inch baking dish. Place in the oven and bake tomatoes filling for 25 minutes.
Remove the biscuit dough from the fridge. On a lightly floured work surface, roll out biscuit dough into a 3/4 or 1-inch thickness. Use a 1 1/2 to 2-inch round biscuit cutter to cut out biscuits. Dip the cutter in flour should it get sticky. Remove the partially cooked filling from the oven and carefully place 6 biscuits atop the tomato filling in the pan. Brush biscuit tops with buttermilk and sprinkle with salt and pepper. Reshape and reroll excess biscuit dough to make extra biscuits at another time. (The shaped biscuit dough freezes very well.)
Return warm filling and biscuit dough to oven and bake for 17-20 minutes, until the biscuits are golden brown and cooked through, and the tomato mixture is bubbling.
Remove from the oven and allow to cool for about 15 minutes before serving. Tomato Cobbler is best served warm.