Cut lobster meat into 1/2- to 1-inch chunks and refrigerate. Place shells on a baking sheet. Add carrots, celery, half the fennel, onion and reserved cobs. Roast 1 hour, turning shells, vegetables and cobs so they don't burn. Ten minutes before removing, spread with tomato paste.
Remove pan from oven and pour liquor onto vegetables, shells and cobs. Transfer to saucepan of reserved broth. Bring to a boil; simmer until reduced by half (8 cups), about 30 minutes. Strain; discard solids.
Thinly slice remaining fennel; add to soup with corn and simmer 10 minutes. Add cream and reserved lobster meat; cook until lobster is heated through, about 5 minutes. Season generously with salt and pepper.