Make the stock: Combine all the ingredients in a pot and cover with 8 cups of water. Bring to a boil, then lower the heat and simmer for 20 minutes. Remove from heat and strain.
Make the matzo balls: In a bowl, combine the eggs with the seltzer, the kale purée and the oil. In another bowl, stir together the matzo meal with the baking powder and salt. Add the dry ingredients to the wet ingredients and stir to combine thoroughly. Refrigerate, uncovered, for 30 minutes.
Using wet hands, and re-wetting hands as necessary, form the matzo ball mixture into 1-inch balls and add to a simmering pot of water for about 20 minutes.
Meanwhile, make the kale broth: Heat the oil and garlic in a pot and add 4 cups of the stock. Once it comes to a simmer, add the kale purée and season with salt to taste.
Using a slotted spoon, transfer matzo balls to bowls (you should have at least 3 per bowl) and serve.