In a medium saucepan, combine the quinoa and 2 cups of water. Bring to a boil, then simmer for 10 minutes. Add the cauliflower, garlic, shallot and simmer another 5 minutes, or until all of the water is absorbed.
Remove from heat and stir in the mozzarella, chopped chipotles, adobo, and salt. Add the chickpeas and egg; use a potato masher or heavy wooden spoon to mash everything together, breaking the chickpeas down into a relatively smooth paste.
Use a teaspoon to form the mixture into rounds; coat with bread crumbs.
In a large pan, heat 2-inches of oil to 275ºF. Add the fritters and cook until golden brown, 1-2 minutes on each side. Remove from the oil and let drain on a cooling rack set over some paper towels.
While the fritters cool, prepare the dipping sauce by mixing together the yogurt, lime juice, and adobo. Add salt to taste.
Serve the chipotle quinoa fritters and dipping sauce warm or at room temperature.