In a 12-inch nonstick skillet over medium heat, melt 1 tablespoon butter. Cook stalks, shallots and garlic, and season with salt, pepper, and nutmeg, stirring 3 to 5 minutes, until shallots are tender. Add broth, cover, and simmer 20 minutes, or until stalks are very tender and liquid has almost completely evaporated. In a food processor, puree until smooth. (May be prepared several hours ahead and refrigerated, tightly covered, until ready to serve.)
Meanwhile, cook florets in boiling salted water 3 minutes, or just until tender. Drain in a colander and shock under cold running water to stop the cooking; drain. (May be prepared several hours ahead and refrigerated, tightly covered, until ready to serve.)
To serve: In a 12-inch nonstick skillet, heat puree just until warmed through. Stir in florets, remaining 2 tablespoons butter, and season with salt and pepper.