Line a baking sheet with parchment paper or a silicone baking mat.
In a large bowl, using a hand whisk (or rubber spatula also works) combine the butter lemon zest and sugars together.
Mix in 1 egg and vanilla extract. Mix until well combined.
In a separate medium bowl, gently whisk together all remaining ingredients (flour, cornmeal, baking soda, cornstarch, baking powder and salt) until fully incorporated.
Add the dry ingredients to the butter and sugar mixture. Using a rubber spatula, fold everything together, gently, until almost combined.
Add the blueberries and gently fold them into the dough. Try not to overmix.
Then using an ice cream scoop, scoop 8 large or 12 smaller cookies and place them onto the baking sheet.
Chill the dough (uncovered) for at least 45 minutes in the fridge.
When ready to bake, preheat oven to 350°F (175°C).
Place 3-4 cookies on a baking sheet (lined with parchment paper) 2-3 inches apart.
Bake for 12-13 minutes (if baking 8 large cookies, they will need about 15-16 minutes).
Let cookies cool on the baking sheet for at least 30 minutes then transfer to a wire rack.
As the cookies cool, work on the blueberry compote.
In a small saucepan, combine the blueberries, 1 tablespoon of the water, sugar, lemon zest, and a small pinch of salt.
Cook over medium heat, stirring occasionally with a wooden spoon, until the blueberries begin to burst and release their juices, about 4–5 minutes.
In a small bowl, whisk together the remaining ½ tablespoon water and cornstarch until smooth.
Stir the cornstarch slurry into the blueberry mixture and continue cooking for 1–2 minutes, stirring constantly, until the compote thickens slightly.
Remove from the heat and allow the compote to cool completely before using.
For the whipped honey buttercream, place butter in a medium bowl.
Using a hand mixer, on medium speed beat the butter until it is nice and fluffy (about 1-2 minutes).
Add the honey, salt and powdered sugar, beat again for another 1-2 minutes until everything is nice and fluffy.
Using a small scoop (or spoon is fine), top the cookies with the whipped honey butter, blueberry compote and sprinkle with sea salt.
