Preheat the broiler. Brush the bread with 1 1/2 tablespoons of the butter. Broil the bread 4 inches from the heat for 1 minute, turning once, until browned. Transfer to plates.
In a large skillet, melt the remaining 2 1/2 tablespoons of butter. Add the apples and cook over moderately high heat, stirring occasionally, until browned in spots, about 5 minutes. Add the sugar and cook over moderate heat, stirring occasionally, until caramelized, 2 to 3 minutes. Add the balsamic vinegar and water and bring to a boil. Simmer over low heat until the apples are tender and the sauce is syrupy, about 4 minutes.
Using a slotted spoon, spoon the apples over the toasts and dollop the ricotta cheese on top. Drizzle with the balsamic-caramel syrup and sprinkle with the almonds. Cut each toast in half and serve right away.