Drain cashews and continue to rinse until the water runs clear (this step is really important).
Drain red pepper and pat dry. Throw it in the blender with the cashews, white pepper and 2T water.
Blend until smooth and add more water if needed.
Season with salt and hot sauce (I used maybe 1/2 teaspoon sriracha) to taste. Your red pepper sauce is done! You'll have some leftover, but it's great as a dip for raw vegetables or tossed with shells and cheese.
To make oats, melt butter in a small pot over medium heat. Add shallot with a big pinch of salt and cook until translucent and slightly soft, about three minutes.
Add oats to pan and make sure they are evenly coated with butter. Stir them around until they are toasted, about five minutes (you'll know they're done when they have the faint smell of popcorn).
Pour in vegetable stock and boil until oats are cooked through.
Grate in cheese to taste, then add more salt if needed. Serve immediately; this does not keep well. For this I really like a hard, nutty cheese like parmesan or pecorino, but a sharp white cheddar would be good, too. I used some Thomasville Tomme from Sweet Grass Dairy since I had it on hand. The amount of cheese you use will depend on the type, so taste as you go.
Steam baby broccoli and follow these instructions for poaching your eggs: https://www.youtube.com/watch?v=nIaQBa7QtRM