Combine ricotta, chicken, spinach, Parmesan and 1 teaspoon rosemary in a medium bowl. Season with salt and pepper, to taste. Set aside.
Divide dough into 6 balls.
Roll each dough ball out on a lightly floured work surface into a 1/4-inch thick circle.
Fill the center of each round with chicken mixture.
Fold round in half and pinch seams together to seal.
Combine butter and remaining rosemary in a small bowl.
Brush butter mixture over each calzone.
Working in batches, place half the calzones into the air fryer.
Set temperature to 375°F/190°C and time to 10 minutes, then press Start/Stop to cook until golden brown. Repeat with remaining calzones.
Serve with marinara sauce.
Tip: Add 1/2 teaspoon crushed red pepper flakes in step 1 for a bit of heat!