Combine prunes and next 10 ingredients (through celery root) in a large oven-proof Dutch oven with a lid. Heat oil in a large, heavy skillet over medium-high heat. Season the beef cheeks on all sides with the salt and pepper. Sear beef on both sides until well browned and caramelized. Add beef cheeks to the top of the prune mixture. Pour beer over beef cheeks, cover and bake for 3 hours or until beef is tender. Remove beef from pan and set aside to keep warm. Strain the braising liquid through a fine-meshed strainer. Discard any solids and transfer braising liquid to a small saucepan. Cook until liquid is reduced by half. Set aside.
Add sweet potatoes to a saucepan and cover with cold water. Bring to a boil and simmer until tender and falling apart. Puree in food processor with heavy cream and season with salt and pepper.
Heat oil in a large skill over medium-low heat. Add onion and cook, stirring often until well caramelized, about 30 minutes.
Blanch rapini in boiling salted water for 2 to 3 minutes. Transfer to icewater to cool. Pat dry and season with salt and pepper.
To assemble, divide sweet potato puree onto 4 plates, place rapini and beef cheeks on each plate, top with caramelized onions and cooking jus.
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