Preheat the oven to 350°F (177°C). Butter a deep pie dish or casserole dish, and arrange cherries in one layer.
In a large mixing bowl, whisk the eggs and sugar together. Add the flour and blend until smooth. Next beat in the melted butter. Slowly add the cream and then the milk. Add vanilla.
Top cherries with egg mixture. Dot the top with pieces of butter.
Bake for 35 to 45 minutes, or until slightly golden around the edges. The custard should be lightly set in the middle. (See note.) Let cool for half an hour, until lukewarm.
Just before serving, sift powder sugar on top. (See note)
Notes
The clafoutis will continue to cook for a while after it is removed. You don't want it to be set too firmly. Serve using a serving spoon, as the result is more of a pudding than a sliceable dessert.