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Combine the flour, baking powder, and salt in a medium bowl.
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In a large bowl, beat the butter and sugar with an electric mixer until light and fluffy, about 2 minutes. Beat in the eggs 1 at a time. Beat in the vanilla extract. Gradually add the flour and beat just until combined. Beat in the crushed pretzels.
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Divide the dough into 2 balls. Wrap in plastic and chill in the freezer for 30 minutes.
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Preheat the oven to 350°F. Line a baking sheet with parchment paper. With floured hands, form each half of dough into a log 12-14 inches long. Transfer the logs to the baking sheet and flatten slightly. Bake until golden-brown and dry to the touch, 30 minutes.
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Remove the baking sheet with the logs from the oven. Reduce the temperature to 300°F. Cool the logs for 30 minutes. Working with one log at a time, transfer to a cutting board and slice on the diagonal into 3/4-1-inch slices. Stand the slices up on the baking sheet.
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Return to the oven and bake for 30 minutes. Transfer the biscotti to a wire rackand cool completely.
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Line a baking sheet with wax paper or parchment paper. Put the chocolate in a large, microwave-safe bowl and microwave in 30 second bursts until melted and smooth. Dip the bottom (flat) side of each biscotti into the melted chocolate. Lay the biscotti flat (cut side down) on the baking sheet. Let stand until the chocolate is set. Transfer to an air-tight container and store at room temperature for up to 3 weeks.