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Step 1
Heat the oven to 350°F with racks in the upper- and lower-middle positions. Line 2 baking sheets with kitchen parchment. In a small saucepan over medium, bring the currants and orange liqueur to a simmer. Cover, remove from the heat and set aside.
Step 2
Meanwhile, in a stand mixer with the paddle attachment, beat the butter and sugar on medium until light and fluffy, 1 to 2 minutes, scraping the bowl as needed. Beat in the zest for about 30 seconds. Mix in the cornmeal, salt, egg yolk and vanilla until combined, about 30 seconds. Add the flour and mix on low until incorporated, another 30 seconds, then mix in the currants and their liquid.
Step 3
Form the dough into 1-tablespoon balls (each about 1 inch in diameter) and space evenly on the prepared baking sheets. Using your hand, flatten each to a 2-inch round about ¼ inch thick. Bake until golden brown at the edges, 15 to 20 minutes, switching and rotating the sheets halfway through. Cool on the sheets for 5 minutes, then transfer to a wire rack and cool completely.