1. Make shrimp butter: heat 2 tablespoons butter in a 10-inch heavy skillet over moderately high heat until foam subsides, then sauté shrimp with salt and black pepper, stirring, until just cooked through, 1 1/2 to 2 minutes. Transfer shrimp with a slotted spoon to a food processor, reserving skillet (do not clean).
2. Cook onion in 1 tablespoon butter in skillet over moderately low heat, stirring occasionally, until softened, 2 to 3 minutes. Scrape onions into processor and cool mixture to room temperature, about 15 minutes.
3. Add lemon juice, cayenne, and remaining 9 tablespoons butter and pulse until shrimp are finely chopped. Pack shrimp butter into a 2-cup ramekin or serving bowl and chill, its surface covered with plastic wrap, at least 6 hours (to allow flavors to develop). Bring to room temperature 45 minutes before serving.
4. Make toast points: put oven rack in upper third of oven and preheat oven to 400°F.
5. Brush 1 side of bread triangles lightly with melted butter and toast, buttered sides up, in a large shallow baking pan until golden around edges, 6 to 8 minutes. Transfer to a rack to cool. Serve toast points with shrimp butter.

Makes 10.

Make Ahead: Shrimp butter can be chilled up to 2 days. Toast points can be made 1 day ahead and kept in an airtight container.