Step 1Cut off fennel stalks and reserve for another use (excellent for fish broths and stews). If there are some attractive feathery fronds, chop and set aside about 2 tablespoons to garnish soup. Quarter bulbs and trim away stems, bottom hard core and any tough parts. Toss 1 tablespoon oil and fennel until well-coated in shallow baking pan just large enough to fit fennel in 1 layer. Roast at 400 degrees until fennel is pale gold, about 20 minutes, then turn and roast 10 minutes longer. Stir in broth, garlic, salt and pepper to taste and 1/2 teaspoon thyme. Cover pan with foil and cook until fennel is very soft, 35 to 45 minutes. Remove foil, stir and roast a few more minutes so most of liquid evaporates.
Step 2Transfer fennel and garlic to food processor and chop coarsely. Add remaining 1/4 teaspoon thyme, salt (it will need about 1 teaspoon), pepper to taste and fennel seeds, if using. With machine on, add remaining 1 tablespoon oil through feed tube.
Step 3Scrape mixture into large bowl. (You should have about 1 cup of puree, so nosh on any extra.) Whisk in eggs, 1 at a time. Add matzo meal and stir well. If you can form a lump into a very soft walnut-size ball (the batter will become firmer when you chill it), don't add any more matzo meal. If necessary, add just enough matzo meal to enable you to do so. Refrigerate 2 to 4 hours so matzo meal can drink in liquid and seasoning.
Step 4Bring 4 quarts water and 1 tablespoon salt to rapid boil in large, wide pot. Dipping your hands into cold water if needed, roll batter into walnut-size balls. When all balls are rolled and water is boiling furiously, reduce heat to gentle boil. Carefully slide in balls 1 at a time and cover pot tightly.
Step 5Simmer over low heat 30 minutes without removing cover. (They will cook by direct heat as well as by steam, which makes them puff and swell, and lifting lid will allow some of steam to escape.) Take out a dumpling and cut it in half. It should be light, fluffy and completely cooked through. If it isn't, continue cooking a few more minutes. Remove balls gently with skimmer or large slotted spoon--they are too fragile to pour into colander.
Step 1Bring broth to simmer in large pot. Add Matzo Balls, mushrooms and asparagus and simmer until vegetables are tender, about 5 minutes.
Step 2To serve, using slotted spoon, divide Matzo Balls among 8 warmed soup bowls and ladle hot soup and vegetables over them. Garnish with the reserved chopped fennel fronds.