Begin by gathering all necessary ingredients. Gently rinse the squash blossoms to remove any dirt or impurities, ensuring to eliminate the stamens, as they possess a bitter taste and are inedible.

Prepare a pot of lightly salted water and bring it to a boil. In a separate large bowl, prepare ice-cold water. Briefly immerse the squash blossoms in the boiling water for 30 to 45 seconds until they slightly wilt; then, use a slotted spoon to transfer them to the cold water immediately. Drain the blossoms on paper towels afterward.

For the filling, combine the goat cheese, Gruyère cheese, egg yolk, black pepper, and cayenne in a mixing bowl. Stir the mixture until it is smooth and homogenous. Transfer this filling into a resealable plastic bag, ensuring to expel the air before sealing. Cut off a small corner of the bag for piping.

Carefully insert the cut corner of the bag into the open end of each blossom. Pipe in approximately one tablespoon of filling, making certain it reaches the base of the blossom. Gently lift the petals to envelop the filling completely, folding any excess petals over the top to secure the filling. Repeat this process for the remaining blossoms and refrigerate them until the cheese is set and firm, at least 30 minutes.

While the blossoms chill, prepare the batter by combining the self-rising flour and cornstarch in a mixing bowl. Gradually whisk in the ice-cold water until the batter achieves a smooth consistency, similar to pancake batter.

Heat one inch of vegetable oil in a cast iron skillet to 350 degrees Fahrenheit (175 degrees Celsius). To test the oil, drop in a small amount of batter; it should sizzle upon contact.

Remove the squash blossoms from the refrigerator and lightly dust them with all-purpose flour on all sides, shaking off any excess. Dip each blossom into the batter, allowing the excess to drip off.

Carefully place about six coated squash blossoms on their sides in the hot oil, frying them until they are pale golden brown—approximately one minute on the first side and 30 seconds to one minute on the other sides.

Transfer the fried blossoms to a plate lined with paper towels to absorb excess oil. Allow them to cool slightly before serving.