Using a stand mixer and paddle attachment cream together softened butter, granulated sugar, and sea salt until smooth and creamy, about 3 minutes. Scrape down sides as needed and continue to mix.
Add in beaten eggs and vanilla and mix until combined, about 1 minute.
Gradually add in 2½ cups of the flour and mix on medium-low until well combined.
Tightly wrap your dough ball in plastic wrap and chill for at least 2 hours. You can separate it into 2 balls if you prefer to work with smaller batches.
Preheat oven to 350°F and line a cookie sheet with parchment paper.
Remove the dough from the fridge.
Use some of the remaining flour to sprinkle on a clean countertop and turn the dough out onto it.
Sprinkle the dough ball with some of the remaining flour and use a rolling pin to roll the dough out to about ¼ inch thick. Use more of the extra flour as needed to keep the dough from sticking to the counter or rolling pin.
Use a large cookie cutter to cut out “panes” of cookie dough and transfer them to the prepared cookie sheet.
Use a smaller cookie cutter to cut shapes in the middle of the panes and remove them. Add the dough that was cut out of the center back to the scrap dough that you will roll out for more cookies or use them for smaller mini cookies.
Place crushed hard candies in the cut-out of the cookie dough panes. You want to fill it nearly full with the hard candy crumbs and be sure it is in an even layer, not mounded in the center.
Bake for 10 to 12 minutes or until the edges of the cookies just begin to brown and the candies are completely melted.
Remove from the oven and allow to cool completely on the baking sheet before removing.