Cut garlic head in half crosswise; rub cut surfaces lightly with olive oil and wrap garlic in foil. Bake in a 400° regular or convection oven until garlic is soft when pressed, about 40 minutes. When cool enough to handle, pluck or squeeze garlic cloves from peel; discard peel.
Meanwhile, in a 6- to 8-quart pan over medium-high heat, cook onion in 1 tablespoon oil, stirring occasionally, until very limp, about 15 minutes (if onion starts to brown, reduce heat and add a few tablespoons of water). Sprinkle with salt and pepper. Add wine and stir often until most of the liquid is evaporated, 2 to 3 minutes.
Add broth, saffron, and carrots. Bring to a boil over medium-high heat, then cover, reduce heat, and simmer until carrots are very tender when pierced, about 20 minutes. Add roasted garlic.
In a blender or food processor, whirl mixture, in batches, until smooth.
Return purée to pan over low heat; add beans and sherry. Cover and simmer, stirring occasionally, about 10 minutes. Add more salt and pepper to taste.