In a medium sized bowl, combine the flour, cornmeal, baking soda, and salt. Whisk the ingredients together until they are evenly distributed. Set it aside for later.
Add the butter, honey, and brown sugar to a large bowl. Cream the ingredients together with an electric mixer until they become light and fluffy. Add in the vanilla extract and egg. Mix until the ingredients are fully incorporated.
Add the dry ingredients into the bowl and mix on low speed. When the ingredients are fully combined, add in the blueberries. Use a rubber spatula to gently fold them into the dough until they are evenly distributed throughout.
Cover the bowl with plastic wrap and refrigerate the dough for 30 minutes.
Preheat the oven to 350˚F. Line a few sheet trays with parchment paper.
Remove the dough from the fridge. Scoop the dough into 2 tbsp sized balls and place them onto the sheet tray, spacing them about 2 inches apart. Bake them in the oven for about 15 minutes. The center should be slightly soft and the edges should have set and turned golden brown.
Remove the cookies from the oven and allow them to cool on the sheet tray for a few minutes before transferring them to a wire rack to cool completely. Once the cookies have scoop a ball of vanilla ice cream and sandwich it with 2 cookies. Repeat this process with the remaining cookies. Enjoy!