Ginger Doughnuts

Whisk together flour, baking powder, baking soda, salt, and 3/4 teaspoon ground ginger in a large bowl.
Whisk together 1 cup sugar and remaining 3/4 teaspoon ground ginger in a shallow bowl.
Pulse remaining 3/4 cup sugar with crystallized ginger in a food processor until ginger is finely chopped. Transfer to a bowl and whisk in buttermilk, butter, and eggs until smooth.
Add buttermilk mixture to flour mixture and stir until a dough forms (dough will be sticky).
Turn out dough onto a well-floured surface and knead gently just until it comes together, 10 to 12 times, then form into a ball. Lightly dust work surface and dough with flour, then roll out dough into a 13-inch round (about 1/3 inch thick) with a floured rolling pin. Cut out rounds with floured cutter and transfer to a lightly floured baking sheet. Gather scraps and reroll, then cut out additional rounds. (Reroll only once.)
Heat oil in a wide 5-quart heavy pot until thermometer registers 375°F. Working in batches of 7 or 8, carefully add rounds, 1 at a time, to oil and fry, turning over once, until golden brown, 1 1/2 to 2 minutes total per batch. (Return oil to 375°F between batches.) Transfer to paper towels to drain. Cool slightly, then dredge in ginger sugar.