Preheat oven to 375°F/190°C. Cover two cookie sheets with parchment paper.
Combine the flax egg and set it aside to thicken. In a stand mixer, add shortening and peanut butter. Beat on medium-high speed for 30 seconds. Add granulated and brown sugar and beat until fluffy, scraping sides of bowl occasionally. Beat in flax egg, milk, and vanilla.
In a separate bowl, combine the flour, baking soda, and salt. Stir to combine. Pour the flour mixture into the peanut butter mixture and beat to combine. If you're using vegan butter instead of shortening, chill the dough for 30 minutes.
Divide the dough into 4 equal parts, then divide those parts into 12 pieces each. Roll the pieces into balls. Roll balls in reserved, granulated sugar to coat. Place rolled balls 1 to 2 inches apart on prepared cookie sheets.
Bake for 6 to 8 minutes, until light brown. Let the cookies cool for a minute then use a small, round cap from your kitchen or your thumb to make an imprint in the center of each cookie. Allow them to cool completely.
To add a vegan chocolate kiss to the center of each cookie, melt 1/4 cup of chocolate chips in the microwave (30 seconds should do it). Then add a dollop of melted chocolate to the imprint of each cookie, followed by a vegan chocolate kiss, lightly pressing them into the melted chocolate. See notes below to substitute vegan ganache.
Store cookies in an airtight container. They will keep at room temperature for 3 to 5 days or in the fridge for up to 10 to 14 days. They can be frozen for up to 2 months.