In a microwave-safe bowl, combine the unsalted butter and semisweet chocolate chips. Microwave in 30-second intervals, stirring in between, until completely smooth and melted. Let the mixture cool for 3 to 4 minutes so it does not cook the eggs.
Whisk the granulated sugar into the melted chocolate mixture until combined. Add the eggs one at a time, whisking well after each addition. Stir in the vanilla extract.
Sift the all-purpose flour, unsweetened cocoa powder, and salt directly into the chocolate mixture. Fold gently with a spatula until just combined - do not overmix or the brownies will be tough instead of fudgy.
Spray a 7-inch round air fryer-safe pan with nonstick cooking spray. Pour the brownie batter into the pan and smooth the top with a spatula.
Preheat the air fryer to 325 degrees F. Place the pan in the air fryer basket and bake for 20 to 24 minutes. The top should look set with a slight jiggle in the center, and a toothpick inserted near the edge should come out with moist crumbs.
Carefully remove the pan from the air fryer and let the brownies cool in the pan for at least 15 minutes before slicing. They will continue to set as they cool. Slice into squares and serve warm or at room temperature.