Chewy Molasses Cookies with Crunchy Lemon Glaze

Make the cookies:

Arrange 2 racks to divide the oven into thirds and heat to 350°F. Line two large baking sheets with parchment paper; set aside.

Place the butter, olive oil, molasses, and brown sugar in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use an electric hand mixer and large bowl.) Beat on medium speed until fluffy and lightened in color. Beat in the the egg until smooth. Beat in the fresh ginger and its juice.

Add the flour, baking soda, cinnamon, ground ginger, salt, and pepper. Beat on low speed until just combined. The dough will be quite soft. Cover and refrigerate the dough at least 30 minutes or up to 3 days.

Pour about 1/2 cup of granulated sugar into a shallow bowl. Divide the dough into 4 portions. Divide the first part into 12 walnut-sized chunks, and roll each into a ball. Roll the ball lightly in the sugar, then place on the baking sheet. Repeat with the second portion of dough, placing the balls on the second baking sheet.

Bake for 6 minutes. Rotate the baking sheets between racks and from front to back. Bake until set, about 6 minutes more. Let the cookies cool on the baking sheets for 5 minutes, then transfer to wire cooling racks and cool completely.

Let the baking sheets cool, then repeat with remaining dough. While the remainder of the cookies cool, make the glaze.

Make the glaze:

Place all the ingredients in a bowl and whisk until smooth. Whisk the lemon juice together with the granulated and powdered sugars. Use immediately.

Using a fork, drizzle the glaze over the cookies in a thin swirl, or paint it on with a pastry brush. Let sit until the glaze hardens.