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Step 1
Position racks in the upper and lower thirds of the oven and preheat to 350º. Line two cookie sheets with parchment paper.
Step 2
Place the butter in a small, heavy-bottomed saucepan set over the lowest possible heat. Add 6 ounces (170 g / 1 cup) of the chocolate and melt together, stirring frequently to prevent the chocolate from scorching. Continue cooking until the mixture is pleasantly warm, but not super hot, to the touch. Remove from the heat and keep warm.
Step 3
In a small bowl, sift together the flour, tapioca flour, and baking powder and set aside.
Step 4
Meanwhile, place the eggs, sugar, and fine salt in the bowl of a stand mixer fitted with the whisk attachment and whip on medium-high speed until the mixture triples in volume and is very light and fluffy, 5 minutes. (You can also do this in a large bowl with an electric egg beater, or a whisk and your buff arms.)
Step 5
Turn the mixer to low and stir in the vanilla until just combined, then the warm (but not too hot!) chocolate/butter mixture.
Step 6
Add the flour mixture and beat on low speed until just combined. Remove the bowl from the mixer and use a flexible silicone spatula to fold in the remaining 4 ounces (115 g / 3/4 cup) chopped chocolate.
Step 7
If the batter is very runny, let it cool for a few minutes until it firms to the consistency of a thick brownie batter. Use a #40 spring-loaded ice cream scoop or 2 spoons to drop heaping tablespoons of batter onto the prepared baking sheets, spacing them at least 2 inches (5 cm) apart. Top each cookie with a few chunks of chocolate and a pinch of flaky salt.
Step 8
Bake the cookies until puffed and cracked and the edges are set, 8–12 minutes, rotating the pans front to back and top to bottom halfway through baking. Let cool slightly and enjoy warm or at room temperature.
Step 9
Extra cookies keep well in an air-tight container for up to 4 days.