Start by combining red rice and water in a heavy 2-quart saucepan with a tight-fitting lid. Bring to a boil over medium heat. Once it reaches a boil, cover and decrease the heat to maintain a gentle simmer. Cook until the rice is tender and the water is mostly absorbed, which should take about 25 minutes. The grains should be fluffy and slightly chewy.
After cooking, drain any remaining water and spread the rice on a sheet tray to cool. This step is crucial as it prevents the rice from steaming further and becoming mushy. Allow it to cool completely before using.
While the rice cools, prepare the honey mustard sauce. In a small bowl, whisk together honey and dijon mustard until well combined. Stir in the chopped gherkin and a splash of Sriracha if you like some heat. Cover and place it in the refrigerator until you’re ready to serve.
Once the rice is cool, transfer it to a large mixing bowl. Add in the shredded beets, crumbled feta, oats, green onions, dill, eggs, and spices: salt and pepper. Using your hands, mix everything until well combined. Don’t be afraid to get in there; it’s a fun process!
If the mixture feels too loose and doesn’t hold together, add additional oats a spoonful at a time until it reaches the right consistency. I usually add about 6 additional tablespoons. The mixture should be moldable without falling apart.
Next, moisten your hands with a little water and use a 1/3 cup measuring cup to form the mixture into cakes, about 2 1/2 inches in diameter. Place each formed cake on a baking sheet. Cover with plastic wrap and chill in the refrigerator for about 30 minutes. This helps the cakes firm up and makes them easier to handle when cooking.
When you’re ready to cook, heat 1 tablespoon of olive oil in a large skillet over medium heat. You’ll know it's hot enough when it shimmers. Carefully add the cakes to the skillet, cooking 4 at a time. Cook until they are golden brown, about 6 minutes per side. Gently flip the cakes halfway through to ensure they cook evenly.
Once all the cakes are cooked, remove them from the skillet and serve them warm or at room temperature. Drizzle or dip them in the chilled honey mustard sauce for a delightful finish!