In a large bowl, combine flour, salt and yeast.

In a medium bowl, whisk together buttermilk, 1/3 cup of the sugar, 4 tablespoons of the oil and egg and then add to flour mixture and stir until combined.

Turn dough out onto a floured surface and knead until very smooth and elastic, about 5 minutes.

Oil a clean, large bowl, arrange dough in the bowl and set aside in a warm spot, covered, until doubled in size, about 2 hours.

On a lightly floured surface, roll out dough to a 12x9-inch rectangle.

Using a round cookie or biscuit cutter, cut into 12 (3-inch) circles and arrange on a parchment-paper-lined baking sheet. (When cutting the donuts, press directly down without turning the cutter. This will help them to rise higher when baking.)

Cover loosely and set aside in a warm spot to let rise for 45 minutes.

Preheat the oven to 350°F.

Bake donuts until puffed and golden brown, 15 to 18 minutes. Set aside to let cool completely.

Using the wide end of a chopstick, make a 1/2-inch hole in the side of each donut, going about 3/4 of the way through.

Spoon jam into a quart-size resealable plastic bag and cut off one corner to make a 1/3-inch opening.

Pipe jam into donuts to fill.

In a medium bowl, whisk together remaining 3 tablespoons oil and 3 tablespoons sugar.

Spread coconut flakes in a wide, shallow dish.

Generously brush the top of each donut with sugar mixture, and then press firmly in coconut, sprinkling more on top. Serve immediately.