Bring 1 inch water to a boil in a small saucepan. Add broccoli. Cover; let steam until soft. Drain. Let cool; finely chop.
Stir together ricotta, broccoli, bell pepper, and carrot in a medium bowl. Spread 1/4 cup ricotta mixture onto 1 slice of bread. Top with second slice. Cut into quarters. Leftover spread can be refrigerated in an airtight container up to 4 days.