Make the miso caramel first. Place the granulated sugar in a small saucepan over medium heat. Let it melt without stirring, swirling the pan occasionally, until it turns a deep amber color, about 4 to 5 minutes.
Remove from heat and carefully whisk in the heavy cream (it will bubble vigorously). Stir in the butter and white miso paste until completely smooth. Pour into a small bowl and refrigerate until thick but still scoopable, about 45 minutes.
In a medium bowl, whisk together the almond flour, cocoa powder, tapioca starch, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and brown sugar together until fluffy, about 3 minutes. Add the egg and vanilla extract and beat until smooth. Gradually add the dry ingredients and stir until just combined. Fold in the dark chocolate chunks.
Scoop 2 tablespoons of cookie dough and flatten it in your palm. Place about 1 teaspoon of the chilled miso caramel in the center. Top with another tablespoon of dough, sealing the caramel completely inside. Roll into a smooth ball. Repeat with the remaining dough and caramel. Place on a parchment-lined baking sheet and refrigerate for 30 minutes.
Preheat your oven to 350F (175C). Arrange the stuffed cookie dough balls 3 inches apart on parchment-lined baking sheets.
Bake for 11 to 13 minutes until the edges are set but the centers still look slightly underdone. Immediately sprinkle each cookie with a pinch of flaky sea salt.
Let the cookies cool on the baking sheets for 10 minutes. When you bite into them, the center will ooze with a savory-sweet miso caramel that perfectly balances the rich dark chocolate.