1. Preheat oven to 350 degrees. Butter a 2-quart shallow baking dish; set aside.

2. Place carrots in a large pot and add enough water to cover by 1 inch. Generously salt water and bring to a boil over high heat. Reduce heat and simmer until carrots are tender and easily pierced with the tip of a sharp knife, about 10 minutes.

3. Strain carrots and transfer to the bowl of a food processor; process until pureed. Transfer carrot puree to a large bowl; stir in milk, cracker crumbs, cheese, onion, butter, salt, black pepper, and cayenne pepper.

4. In the bowl of an electric mixer fitted with the whisk attachment, whisk eggs until foamy. Whisk eggs into carrot mixture until just combined.

5. Transfer carrot mixture to prepared baking dish and bake until puffed and light golden brown on top, 40 to 45 minutes; serve warm.