Mix together all ingredients together seasoning with salt and pepper, to taste.
Heat a grill pan or griddle, add 1 Tb. butter. Add a tortilla and cook it on one side until it puffs (about 30 seconds).
Flip tortilla over and sprinkle over entire surface 1/4 cup of squash blossom filling.
Top with another tortilla, and after cheese has melted and the two tortillas stick together (a couple of minutes), flip quesadilla and cook for a couple of minutes more.
Repeat for the remainder of the filling and tortillas.
For the Tomatillo Salsa
Place all ingredients in a blender or food processor and pulse to combine. Blend on low speed until a coarse puree is formed.
Pour into a bowl, taste and add more salt or lime if desired. Salsa can be thinned with a bit of water if desired.