Preheat oven to 300°. Spread bread cubes on a parchment-lined rimmed baking sheet. Toast until well browned and crisp, about 20 minutes, stirring halfway through. Sift powdered sugar with cinnamon into a bowl. Add croutons and toss to coat.
Put a scoop of ice cream in each of 8 to 10 shallow bowls; sprinkle with lime zest. Keep frozen on a rimmed baking sheet until ready to serve.
Turn off any overhead fans. Divide ingredients for bananas in half (to cook in two batches) and arrange next to burner (combine liquors, then divide in half). Remove four ice cream bowls from freezer and surround each scoop with about 1/4 cup croutons.
Heat a large frying pan over medium-high heat. Add butter and brown sugar and cook until they've fused into a golden brown, thick, bubbling caramel sauce, about 3 minutes. Add salt and bananas. Turn bananas several times to coat in caramel sauce.
Remove pan from heat and pour in liquor. Standing back, ignite with lighter (flames will shoot up). Immediately sprinkle with 2 shakes of cinnamon to create sparks.
Set pan back over medium-high heat (alcohol will flare up again). Stir in lime juice and cream, then let sauce cook, stirring with spatula occasionally, until bubbling and slightly thickened, 1 minute.
Spoon sauce and bananas into bowls, around ice cream. Zest half of lime over bowls and serve immediately.
Wipe out pan with paper towels and make a second batch of bananas Foster with remaining ingredients.
*Alfred's uses the 15.000 BTU Iwatani 35FW portable butane stove, approved for indoor and outdoor use; find at amazon.com ($75).
Make ahead: Croutons, up 1 week, kept airtight at room temperature. Scoop ice cream up to 1 day ahead and sprinkle with zest, and peel bananas up to 1 day ahead, wrap in plastic wrap and keep at room temperature, then slice just before cooking.