For doughnuts: In a large bowl, beat butter, sugar, and vanilla with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add egg, beating until thick and pale, about 2 minutes. Beat in sour cream.
In a medium bowl, whisk together flour, baking powder, pumpkin pie spice, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined. Wrap dough in plastic wrap (dough will be slightly sticky). Refrigerate for at least 30 minutes or up to 1 hour.
On a lightly floured surface, gently knead dough 3 to 4 times. Roll dough to ½-inch thickness. Using a 3-inch doughnut cutter, cut dough, rerolling scraps as necessary.
Fill a Dutch oven halfway full with oil, and heat over medium heat until a deep-fry thermometer registers 350°. Add doughnuts to hot oil in batches; fry until golden brown, about 1 minute per side. Let drain on paper towels; let cool.
For glaze: In a medium bowl, whisk together confectioners’ sugar, orange juice, and salt until smooth. Dip doughnuts in glaze; sprinkle with pecans. Let stand on a wire rack until glaze is set.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/spiced-cake-doughnuts-recipe/