In a bowl, combine the water and yeast. Let rest for 5 minutes.
In a stand mixer fitted with the dough hook or in a large bowl with a wooden spoon, combine the flour, sugar, yeast mixture, baking powder and salt. Add the eggs and vanilla. Mix just until the dough starts to form.
Mix in the butter. Knead the dough vigorously with the dough hook or with your hands on a lightly floured work surface until smooth, about 5 minutes. Form into a ball and place in a clean, lightly floured bowl. Cover with a slightly damp cloth and let rise in a warm, humid spot for 2 hours or until doubled in volume.
On a lightly floured work surface, using a rolling pin, roll the dough out to ½ inch (1 cm) thick. Using a 3 ½-inch (9 cm) round cookie cutter, cut out 10 doughnuts. Cover the doughnuts and dough scraps with a clean cloth and let rest for 15 minutes.
Preheat the oil in the deep fryer to 350°F (180°C). Line a baking sheet with paper towel or a wire rack.
Place some sugar in a bowl and set aside.
Fry 2 to 3 doughnuts at a time in the hot oil for 1 minute on each side or until golden. Drain on the paper towel or wire rack. Coat the warm doughnuts with the sugar. Let cool completely, about 1 hour. Repeat with the remaining doughnuts and dough scraps (see note).
In a bowl, beat the cream and sugar with an electric mixer until firm peaks form.
Using a knife, cut the doughnuts in half horizontally. Fill each doughnut with about ¼ cup (60 ml) of the ice cream, ¼ cup (60 ml) of the sorbet and whipped cream. Serve immediately.
You can make use of the dough scraps by frying them as is. Move over doughnut holes, hello doughnut frames!
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.