Place the unwrapped peppermint Kisses on a plate and chill in the freezer for 10–15 minutes so they keep their shape when added to warm cookies.
Preheat the oven to 325°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cocoa, espresso powder, baking soda, and salt; set aside.
In a large bowl with a hand mixer (or stand mixer with paddle), beat the softened butter with granulated sugar and brown sugar on medium-high until very fluffy and slightly lightened, 3–4 minutes. Scrape the bowl as needed.
Beat in the egg, then the egg yolk until smooth. Mix in vanilla and peppermint extract (if using).
Add the dry ingredients to the bowl and mix on low speed just until no dry streaks remain. The dough will be soft and thick.
Let the dough rest at room temperature for 10 minutes to hydrate the cocoa and make scooping easier.
Scoop dough into 1½-tablespoon portions (about a #40 scoop), roll into balls, then coat in coarse sanding sugar. Arrange 2 inches apart on the prepared sheets.
Bake one sheet at a time for 10–12 minutes, rotating the pan halfway, until the edges are set and the centers look slightly soft.
Cool on the pan for 2 minutes, then gently press one chilled peppermint Kiss into the center of each cookie. Let stand on the pan until the chocolate firms up (or slide the pan into the fridge for 5 minutes to speed it along).
Repeat with remaining dough and candies. Cool completely before storing.