Combine all ingredients for the chipotle cheese in a blender jar and process on high until smooth. Adjust the consistency adding one tablespoon of water at a time until desired thickness is achieved. Remove from the blender jar and set aside.
Rinse the quinoa in a fine mesh strainer and transfer to a clean blender jar. Add the water and blend on high speed until smooth. Add extra water as needed until the mixture is the consistency of pancake batter. Transfer the batter to a bowl.
Rinse and pat dry the squash blossoms and basil. Tear the basil leave in half and place one half a leaf inside each blossom. Add a heaping teaspoon of the chipolte cheese and gently pinch the blossom to seal it.
Heat a frying pan with 1 tablespoon of oil on medium high. Dredge the first ten blossoms in the quinoa batter and place them in the hot frying pan. Turn after 2-3 minutes and continue cooking until they are golden brown on all sides. Transfer to a paper towel to cool.
Add the additional tablespoon of oil and fry the remaining blossoms. Serve warm.