In a large bowl or stand mixer fitted with a paddle attachment, cream together the butter, sugar, and vanilla paste on medium speed until light and fluffy. About 3 to 5 minutes. Scrape down the sides of the bowl as needed.
With the mixer on low speed, slowly add the flour and mix just until blended.
Fold in the chopped chocolate just until combined.
Divide the dough in half on two large pieces of parchment paper. The dough will be crumbly.
Use your hands to shape each half of the dough into a log. Use the parchment to help you roll and round out the log.
Sprinkle about ¼ cup of coarse sugar on each of the parchment papers and roll the logs in it.
Roll the cookie dough logs up in the parchment paper and refrigerate for at least 2 hours.
After the dough has chilled, unroll and slice each log into 12 even slices.
Preheat oven to 350°F. Arrange the cookies on a parchment-lined baking sheet about 1 inch apart (these cookies don't really spread) and sprinkle with flaky sea salt.
Bake for 12 to 15 minutes until the edges are golden brown and the chocolate in the center is shiny.