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In a large mixing bowl, combine all of the ingredients for the meatballs and mix well to combine (note that the mixture will be rather wet at first as a result of all the eggs - just keep mixing it and it will come together). Using a large spoon or ice-cream scoop, portion the mixture into large meatballs (about 1/4 cup each) and arrange on the prepared baking sheet. Bake the meatballs until golden brown and cooked through, 22 to 25 minutes.
While the meatballs are baking, place a medium pot over medium heat with the butter. Add the caraway seeds to the melted butter and toast until aromatic, about 1 minute. Sprinkle the flour over the butter and cook, stirring well, to make a smooth paste, about 1 minute. Add the beef stock to the pot and bring the liquids up to a bubble, whisking frequently. Reduce the heat to medium-low and simmer the gravy, stirring occasionally, until thickened and aromatic, about 10 minutes. Season with salt and pepper.
BONUS: I like to round this meal out with a simple kale salad. My favorite dressing for it is a creamy tahini-lemon blend that's super easy to make. In the jar of blender, combine 1/4 cup tahini, 1/4 cup water, 1/4 cup lemon juice, 2 grated cloves garlic and some salt and pepper. Blend to a smooth paste, adding a splash of water as needed to loosen the mixture.