Step 1

Arrange a rack in the middle of the oven and heat the oven to 350°F. Coat a 9x13-inch baking dish generously with butter.

Step 2

Halve the fruit, then remove and discard the pits. Cut into 1/2- to 3/4-inch-thick slices. Place in the baking dish and arrange into a single layer; set aside.

Step 3

Combine the eggs, sugar, cardamom, and salt in a large bowl and whisk until smooth and the sugar is dissolved. Add the flour and whisk until just smooth. Add the milk, 3 tablespoons butter, and vanilla and whisk until just combined. Slowly pour over the fruit (to prevent the fruit from floating) in the prepared baking dish.

Step 4

Bake until set, puffed, and light golden-brown around the edges, about 50 minutes. Place the baking dish on a wire rack and let cool for 15 minutes (the clafoutis will deflate). Cut into squares, dust with powdered sugar if using, and serve warm.