Cover the rice with 2” of water. Bring to a boil, reduce to a simmer, cover, and cook until the rice is cooked; 45 minutes or so.
In the food processor, pulse the garlic into small pieces. Add the oats, cilantro, salt, and pepper until the oats are in fine pieces. Add in the brown rice and carrots, followed by the ricotta and eggs. Pulse the mixture a few times to combine the mixture. The carrots and brown rice should still be visible but broken down slightly.
Place mixture in the refrigerator and allow to sit for 30 minutes.
Warm the olive oil up over medium heat in a large skillet with lid. Wet your hands and form the mixture into patties that are roughly 1" thick and 4" wide. Place in the skillet and cook for 4 minutes, until browning and crisp. Flip, cover, and cook for another 4 minutes until crisp and warmed through.
To make the sauce: combine the ingredients for the sauce in a food processor or blender. Puree until smooth, taste, and add more salt as desired.