Heat the olive oil in a large skillet. Add the onion, season with salt and pepper and cook over moderate heat, stirring occasionally, until just softened, about 5 minutes. Add the paprika, cover and continue cooking another minute.
Add the brussels sprouts to the skillet and cook, stirring only to prevent scorching, until tender throughout and browned in spots, about 10-15 minutes. Season to taste with salt and pepper.
Arrange the toasts on a baking sheet and top with the cheddar. Bake for 2 minutes, until the cheese is melted; mound the brussels sprouts and onions on top and serve.
Recipe by Sprung At Last at https://sprungatlast.com/2015/03/deborah-madisons-brussels-sprouts-and-smoky-onions-on-cheese-toast/