1. Cover dried mushrooms with 1 1/2 cups boiling water in a heatproof bowl; let soak 20 minutes. Using a slotted spoon, transfer mushrooms to a cutting board and roughly chop. Strain soaking liquid; add to a large pot along with stock, milk, and cardamom. Bring to a low simmer over medium heat and keep stock warm.

2. Heat 2 tablespoons butter in a medium pot over medium-high. Add wild mushrooms and chopped dried mushrooms. Season with salt and pepper and cook, stirring occasionally, until golden, about 3 to 4 minutes. Use a slotted spoon to remove mushrooms from pan; set aside.

3. Melt 1 tablespoon butter in same pot over medium heat. Cook garlic, shallot, leek, coriander, and red-pepper flakes until vegetables are tender, about 5 minutes. Stir in orzo until well combined.

4. Ladle 2 cups reserved stock over orzo and cook, stirring often with a wooden spoon, until almost completely absorbed. Continue adding stock, 1 cup at a time, stirring often and waiting for each addition to be almost completely absorbed before adding the next, until orzo is just al dente, about 20 minutes. Stir in sauteed mushrooms and continue to cook, stirring, for 2 minutes.

5. Remove from heat and stir in fava beans, 1/4 cup parsley, 2 tablespoons dill, lemon zest and juice, and remaining 1 tablespoon butter. Season with salt and pepper. Spoon orzo into serving bowls, top each with a soft-poached egg, and sprinkle with remaining herbs.