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Beat together butter, oil, vanilla, zest, and 3/4 cup powdered sugar in a large bowl with an electric mixer on medium speed until light and fluffy, 2 to 3 minutes. Beat in egg yolk. Add flour mixture; beat on low speed just until combined. Stir in nuts.
Shape dough into 32 balls (1 tablespoon each). Arrange dough balls 2 inches apart on 2 baking sheets lined with parchment paper. Bake at 350°F until set and lightly browned on bottom, 12 to 14 minutes. Cool on baking sheets set on a wire rack for 3 minutes. Transfer cookies directly to wire rack to cool completely.