Season the short ribs all over with salt and pepper then dust with flour. Heat a 7-quart Dutch oven over medium-high heat, add the olive oil and heat through. Working in batches, sear the ribs on all sides, about 5 minutes total. Remove to a plate and repeat with the remaining ribs.
Heat oven to 325ºF (170ºC).
Return the pot to medium heat and add the shallots sautéing until tender, about 3 minutes. Add the short ribs back to the pot along with the blackberries. Pour the wine into the pot and bring to a boil then move the pot to the oven.
Cook, turning the ribs occasionally, until the meat is fork tender and the sauce has a syrupy consistency, about 3 to 3½ hours.
For the whipped ricotta:
Add the ricotta, olive oil and maple syrup to the bowl of a food processor fitted with a blade attachment. Pulse until the ricotta is smooth then remove to a bowl and store, refrigerated until ready to use.
For serving:
Heat oven to 400ºF (200ºC). Toss the beets in the olive oil season with salt and pepper then wrap in aluminum foil and arrange on a baking sheet. Roast until tender, about 50 to 60 minutes.
Spread a spoonful of the whipped ricotta on plates and arrange beets around the plate. Top with beef short ribs and a spoonful of the blackberry sauce. Garnish with additional blackberries and arugula (optional). Serve immediately.