Preheat the oven to 350 degrees F. Season the short ribs with salt and pepper. Heat the olive oil in a Dutch oven or ovenproof pot over medium-high heat. Add the short ribs and brown on all sides, about 10 minutes total. Transfer the meat to a plate.
Add the onions, garlic, chopped celery stalks and paprika to the pot and cook, stirring occasionally, until the onions soften, about 4 minutes. Add the tomato paste and cook, stirring, until it starts to brown, about 4 minutes. Add 6 cups water and 2 teaspoons salt and stir, scraping up any browned bits from the bottom of the pot. Return the meat to the pot and bring to a simmer. Cover, transfer to the oven and cook 1 hour, 30 minutes.
Meanwhile, puree the chopped chard, lemon juice, scallions, celery leaves, 1 1/2 cups water and 1 teaspoon salt in a blender until smooth. Remove the pot from the oven; stir in the chard puree, beets, carrots, sweet potatoes and sugar. Return the pot to the oven and cook, uncovered, until the meat and vegetables are tender but hold their shape, 1 hour, 30 minutes to 2 hours. Remove the bones from the short ribs; skim the fat off the sauce. Season with salt and pepper. Ladle the meat, vegetables and sauce into shallow bowls.