Preheat your oven to 350°F (175°C) and lightly grease a baking dish.
Boil carrots until tender, then drain and let them cool slightly.
Blend cooked carrots with butter and vanilla until smooth.
Add eggs one at a time, blending well after each addition.
In a separate bowl, mix flour, baking powder, salt, and sugar.
Combine the dry ingredients with the carrot mixture and blend until fully incorporated.
Pour the batter into the prepared dish and smooth the top.
Bake for 40–45 minutes, or until puffed and golden around the edges.