In a large bowl, stir together rice, hot sauce, garlic powder, chile powder, cheese, and jalapeño. Place in refrigerator for 30 min to chill.
While the rice is chilling, create the avocado cilantro sauce. Add avocados, cilantro, sour cream, salt, pepper, garlic powder, lime juice, and cayenne to a food processor or blender and puree until smooth. Refrigerate until ready to serve.
Prepare your dredging stations by setting out 2 bowls. In one bowl, add eggs and lightly beat them. In the second bowl, add the breadcrumbs.
Heat up enough oil for frying in a heavy bottom pan (my oil was about 2” to 3” deep). Heat your oil to 375°F, or, if you don't have a thermometer, once the oil begins to shimmer, drop in a test couple grains of cooled rice — if they start to sizzle, the oil is ready!
Remove rice mixture from refrigerator. Form balls of rice in your hands, packing them tightly. My arancini were about 1 1/2 to 2 inches thick. Dip each ball of rice into the breadcrumbs, then the egg, then the breadcrumbs again before carefully adding to the hot oil. Fry until golden brown, approximately 2 minutes, remove from oil and set on paper towels to drain. Repeat in batches of 3-4, making sure you do not overcrowd the pan.