In a large bowl, whisk together the flour, cocoa powder, baking powder, cinnamon, and salt.
Put the olive oil and sugar in a medium mixing bowl, and beat with a hand mixer until smooth and light. Add the eggs and egg yolk, one at a time, beating until smooth. Add the milk beverage and vinegar, and beat until smooth.
With the mixer on low speed, gradually add the flour mixture, and beat just until the dough is combined. Stir in the chocolate chips.
Cover the bowl with plastic wrap and refrigerate the dough for at least 4 hours.
Preheat your oven to 325ºF and grease two large baking sheets or line them with parchment paper.
Turn the dough out onto a lightly floured surface, and divide it into quarters. Roll each piece of dough into log, about 1½ inches in diameter. Place the logs on your prepared baking sheets, leaving space in between.
Bake for about 30 minutes, or until golden and set. Remove the biscotti logs to a wire rack and let cool for 10 minutes.
Reduce the oven temperature to 300ºF.
Place a log on a cutting board and cut diagonally into ¾-inch wide slices with a serrated knife. Place the slices, cut-side down, on your prepared baking sheets. Repeat with the 3 remaining logs.
Bake the chocolate biscotti for 15 to 18 minutes, or until toasted. Remove the biscotti to wire racks to cool completely and crisp up.
Notes
Mexican Chocolate Variation: Increase the ground cinnamon to 1 teaspoon and the salt to ½ teaspoon. Omit the balsamic vinegar, but increase the milk alternative to 6 tablespoons and add 1 teaspoon vanilla extract. If you're feeling spicy, you can add ⅛ teaspoon cayenne pepper with the cinnamon.