Trim stalks from fennel and reserve 3/4 cup feathery leaves. Trim root ends and discard tough outer portions. Halve fennel lengthwise (to make flatter rather than taller pieces).
Lay fennel cut-side up in a 12-in. frying pan. Add chicken broth. Cover and bring to a boil over high heat; then reduce heat and simmer until fennel is just tender when pierced, 9 or 10 minutes.
Preheat oven to 375°. With a slotted spoon, transfer fennel, cut side up, to a shallow 2 1/2- to 3-qt. baking dish (it should fit snugly). Boil chicken broth, uncovered, over high heat until reduced to 1/3 cup, 5 to 8 minutes. Coarsely chop half of reserved fennel leaves and add to broth; spoon over fennel.
In a bowl, gently mash cheese and panko with a fork until blended (if using gorgonzola, squeeze handfuls together and break into clumps). Dot over fennel, leaving some of fennel uncovered.
Bake until cheese browns and fennel is hot, about 25 minutes. Scatter remaining fennel leaves on top.
MAKE AHEAD Through step 4, chilled airtight up to 1 day (chill remaining fennel leaves separately); bake about 35 minutes.