Fill 1 large chimney starter with charcoal briquettes and light. Once the coals are ashy white, transfer to a kettle grill and spread evenly. Set grate over coals.
Lightly brush all sides of fruit with oil and grill for 1 1/2 minutes on each side. Remove from the grill to a cutting board, and cut into 1/2-inch pieces. Lightly oil the bottom and sides of a Dutch oven and spread the fruit evenly over the bottom.
In a medium mixing bowl, whisk together the eggs and sugar until frothy and lightened in color, 2 to 3 minutes. Add the flour and whisk just to combine, followed by the milk and vanilla. Pour the batter over the fruit and cover with the lid. Carefully set 22 to 23 coals on the lid and leave only 18 to 19 coals under the grate. If you have more coals than this, remove them from the grill or push them to the edges so they are not directly under the Dutch oven. Set the Dutch oven on the grate, 2 inches above and directly over the coals. Cook until the top is golden brown and a knife inserted in the middle comes out clean, 20 to 25 minutes. Allow the clafoutis to cool for 30 minutes before removing from the Dutch oven to a serving plate. Slice and serve.