In a small pan, stir 1/2 cup brown rice and 1 cup water, and add 1/8 tsp salt. Bring to a boil, cover, and cook for about 20 minutes, until tender. Remove the lid and set it aside.
Cauliflower Filling
Heat 1 tsp olive oil in the skillet, add three sliced scallions, sautee for a couple of minutes, then add all the cauliflower (3 cups chopped florets), season with a pinch of black pepper and 1/4 tsp salt, and stir. Cover on medium heat, stirring occasionally, and cook until tender.Once the cauliflower is tender, spoon the cauliflower into another dish and set aside.
Asparagus
Add 1/2 tsp olive oil into the skillet (use the same skillet you used for cauliflower), add sliced asparagus (10 stalks), season with a pinch of pepper and salt, add diced garlic, and cook for one minute on medium-high, stirring. Remove from heat, and set aside.
Semolina
In a medium saucepan, bring 1/2 cup milk, 3/4 cup water, 1 teaspoon olive oil, and 1/4 tsp salt to boil. Watch it, it can boil over. Remove from heat, add 8 tablespoons of semolina, and stir, whisking until smooth. Return to heat, and cook until thick, 5-7 minutes, stirring constantly. Remove from the heat, and stir in 2 tablespoons of chopped parsley, 1/4 cup coarsely grated parmesan cheese and cooked brown rice. Taste, season with pepper and salt if desired. Set aside to cool slightly for about 10 minutes.Into the semolina mixture, stir in 1 whole egg, add the asparagus and cauliflower mixture, and stir well.
Chilling
Spoon the thick mixture into a square baking pan lined with wax paper. Make the layer about 1 inch thick. Cover the pan with plastic wrap, and refrigerate for 2 hours or overnight.Cut the chilled cake into squares, about 2½ by 2½-inch.
Breading
Whisk together 3 egg whites and 1 tbl of water, until foamy.
In a shallow dish, stir together 1½ cups breadcrumbs and 1/2 quick oats (if using), season breadcrumbs with a pinch of salt and pepper.
Using a spatula, lift the cakes from the baking pan, and dip them in the egg-white mixture. Use your hands to dip the cakes and turn them so they are fully coated with the egg white. Let the excess drip back into the egg white mixture, and then coat each patty in the breadcrumbs mixture. Transfer to a clean plate. Repeat.
Cook Cakes
In a large skillet, heat olive oil, about 3 tablespoons, Once hot, lower the temperature to medium. Carefully add cakes and cook for about 5 minutes on each side until golden brown. Use a silicone spatula and a turner to flip them over.If needed, add additional oil between batches.
Once cooked, transfer the cakes onto a baking sheet lined with a paper towel to absorb oil.
Serve hot or lukewarm.
These savory cakes can be made ahead and reheated in the oven at 350 F for 10 minutes.