Place first 6 ingredients into a food processor and blend until smooth. Season with salt and pepper, stir together and transfer into a piping bag (or a reusable plastic bag).
Pipe about 1 ounce of cheese filling into the cavity of each squash blossom and gently push together until closed. Set aside.
Place all tempura ingredients into a mixing bowl and stir together until no lumps remain. Carefully dip each stuffed squash blossom into the batter and gently shake to remove the excess. Gently dip each blossom into the oil and fry for 2 to 3 minutes or until the batter has puffed and begins to barely turn golden brown. Remove from oil and drain into a paper towel for 1 minute. Transfer blossoms onto a cooling rack lined with a baking sheet and season with salt and pepper. Serve immediately.