Wrap coffee beans and cinnamon stick in a 4-inch square of cheesecloth, tying the bundle closed with kitchen twine. Grease
a (8-inch) square baking pan with butter.

In a large saucepan, combine spice bundle, 1 1/4 cups water, milk, butter, and 1/8 teaspoon salt; bring to a boil. Remove and discard bundle, then slowly add polenta in a thin stream, whisking; reduce heat to low and cook, whisking constantly, for 2 minutes. Continue to cook on low, stirring often with a wooden spoon, until thickened and tender, about 40 minutes. Remove from heat; mix in egg yolks and 2 tablespoons sugar.

Transfer polenta to prepared pan and spread evenly with a rubber spatula. Let polenta cool completely in pan on a wire rack.

In a medium skillet, combine apple, wine, 1/4 cup sugar and 1 tablespoon water; bring to a simmer and cook, stirring frequently, until apples are soft, 6 to 8 minutes. Transfer apple mixture to the bowl of a food processor. Add lemon zest and remaining tablespoon water; purée until smooth.

When polenta is cool, turn out onto a cutting board. Cut into 1/2- x 2-inch strips.

Line a large plate with paper towels. Spread flour on a second plate. Roll strips in flour to lightly coat.

In a large wide pot, heat 3 inches oil over medium-high heat until thermometer registers 375º. Working with about 8 pieces at a time, fry strips until golden, 45 seconds to 1 minute per batch. Using a slotted spoon, transfer fried strips to paper towels to drain, then dust with confectioners sugar. Serve warm or at room temperature, with applesauce.