In a small sauce pot, combine the shiitake mushrooms and 2 cups [4 cups] water. Bring to a boil, cover, and cook, stirring occasionally, until softened, 3 to 5 minutes.
Meanwhile, prepare the meatballs.

• Peel and finely chop enough shallots to measure ¼ cup [½ cup].
• Cut a small corner from the ground beef packaging and drain off any excess liquid. Transfer to a plate; pat dry with a paper towel.

In a large bowl, using a fork or whisk, blend the egg with the shallots and mushroom-herb blend. Add the ground beef, season generously with salt and pepper, and mix until just combined. Using wet hands, form the mixture into 1-inch meatballs.

• Finely chop, press, or grate the garlic.
• Remove the mushrooms, reserving ⅓ cup [⅔ cup] soaking liquid. Discard the stems and thinly slice the mushroom caps.

In a large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the meatballs and cook, turning occasionally, until lightly browned but not yet cooked through, 3 to 5 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Add the mushrooms, reserved soaking liquid, tomatoes, and vegetable broth, and season with salt and pepper. Bring to a boil, then reduce to a simmer and cook, stirring occasionally, until the meatballs are cooked through and the ragu has thickened slightly, 5 to 6 minutes. Remove from the heat and season to taste with salt and pepper.
Meanwhile, prepare the garnish and cook the cabbage.

• Strip the parsley leaves from the stems; coarsely chop the leaves for garnish.
• Cut away any core from the cabbage; thinly slice the cabbage.

In another large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the cabbage, season with salt and pepper, and cook, stirring occasionally, until just wilted, 2 to 3 minutes. Remove from the heat and season to taste with salt and pepper.

Transfer the cabbage to individual plates. Top with the meatballs and tomato-shiitake ragu, garnish with the parsley, and serve.