Stir together ½ cup flour and yeast in bowl of a stand mixer. Stir in milk until fully combined. Cover with plastic wrap and let sit for 10 to 15 minutes, until foamy and bubbly. Discard plastic wrap.
Step 1. Add eggs to bowl. Fit mixer with paddle attachment and mix on medium speed until smooth. Add remaining 3¼ cups flour, sugar, and salt and stir on low speed for about 2 minutes, until ingredients are fully incorporated. Turn off mixer and replace paddle with dough hook.
Step 2. Return mixer to medium speed and add butter in 4 portions, beating until each addition is thoroughly combined before adding the next.
Step 3. Reduce speed to low and mix dough for about 7 minutes, or until it’s smooth and stretchy and begins to pull away from the sides of the bowl. Transfer to a lightly floured work surface and knead gently for 1 minute before shaping into a ball.
Step 4. Lightly oil a medium bowl and transfer dough to bowl. Rub top of dough with a bit of oil and cover bowl with plastic wrap. Let rise in a warm, draft-free spot for 1 hour, then refrigerate for at least 12 hours.
Step 5. Dust a work surface with flour. Remove dough from refrigerator and roll into a ½-inch-thick round. Use a 3-inch biscuit cutter to stamp out 9 rounds of dough. Transfer to a floured baking sheet, cover with plastic wrap, and let rise in a warm, draft-free spot for 2 to 3 hours, until pillowy and doubled in height.
Step 6. When ready to fry, heat canola oil to 350°F in a large, heavy-bottom pot (a Dutch oven works well) or deep fryer. Place a wire rack on a rimmed baking sheet and pour about ¾ cup granulated sugar into a medium bowl. Set aside.
Step 7. Fry doughnuts, 3 at a time, for 2 to 3 minutes on each side, until medium golden brown. Transfer to prepared wire rack with a slotted spoon and repeat until all doughnuts are fried. Toss each doughnut in the bowl of sugar to coat; shake off excess, and return to wire rack.
Step 8. Mix Fromage Blanc and maple syrup together in a small bowl, then transfer to a pastry bag fitted with a wide tip (or use a sealable plastic bag with the corner snipped off).
Step 9. When doughnuts have cooled, cut a ½-inch slit in the side of each doughnut and pipe about 2 tablespoons of filling into each doughnut. Serve within a few hours of making.