Melt 2 teaspoons butter in a medium nonstick skillet over medium-low heat. Add banana quarters, cut-side down; sprinkle with 1 tablespoon brown sugar. Cook, stirring gently to prevent the bananas from sticking and flipping once, until browned and softened, about 10 minutes. Transfer the caramelized bananas and any liquids to a mini food processor; let cool for 5 minutes.
Add 1 teaspoon cinnamon, ¼ teaspoon salt, ⅛ teaspoon nutmeg and the remaining ½ cup softened butter to the bananas in the processor; process until smooth, about 30 seconds. Serve with toast, if desired.
