Place all the ingredients in a bowl and mix well (TIP: if mixture seems dry, add another egg - it should hold together, but not be too runny).
Heat oil on a nonstick griddle or in a pan over medium-high heat.
Using a 1/4 cup measure, place a dollop of rice mixture on the griddle/pan, then use the back of the cup to flatten into a patty. Repeat with remaining rice mixture.
Cook the first side until golden brown, about 3-5 minutes, then flip and cook the other side until brown.
Serve immediately or see notes for storage options.
Notes
*Gluten Free Variation: Omit the bread crumbs and increase the cheese to 1 cup. Proceed with recipe as normal.Storage & Make Ahead: Cover cooled patties and refrigerate until needed up to 5 days (or even freeze for longer storage, up to 5 months), reheating them in a 350 degree oven (or on the grill) for a few minutes until warm and crisp.More Variations:
Add dried or fresh herbs to the mixture before cooking.
Use a different cheese: cheddar, gouda, pepper jack, havarti, etc.