Heat milk, cream, and 1 Tbsp. water in a small saucepan until an instant-read thermometer registers 110°–115°. Transfer to a small bowl and stir in a pinch of sugar. Sprinkle yeast over. Let stand until foamy, about 10 minutes.
Using an electric mixer, beat remaining 1/3 cup sugar and eggs in a large bowl until pale and foamy, about 3 minutes. Gently stir in yeast mixture and melted butter. Add 2 cups flour and salt; stir until a very soft dough forms.
Cover bowl with a clean kitchen towel. Let dough rise in a warm, draft-free area until doubled, about 1 1/2 hours. (Alternatively, cover bowl loosely with plastic wrap and allow dough to rise for 8 hours in the refrigerator.)
Punch down dough and knead several turns in bowl; form into a ball. Transfer to a generously floured work surface. Sprinkle dough with flour and roll out to 1/2" thickness. Cut out doughnut holes with cookie cutter. Transfer to a floured baking sheet. Cover with a kitchen towel and let rest for 20 minutes.
Pour syrup into a large bowl. Attach deep-fry thermometer to the side of a large pot; pour in oil to a depth of 2" and heat over medium heat until thermometer registers 350°. Working in batches, fry doughnuts, stirring gently with a slotted spoon to keep doughnuts rotating, until golden brown, about 2 minutes per batch. Using slotted spoon, transfer doughnuts to bowl of maple syrup; let soak, turning as more doughnuts are added, until doughnuts absorb syrup, about 15 minutes.