In a large skillet, brown the breakfast sausage over medium/high heat, breaking it up with a spoon as it cooks. Cook until it looks crispy and has released a good amount of fat. Using a slotted spoon, transfer the browned sausage to a separate bowl, leaving the grease behind in the pan.
Turn the heat to medium and add one layer of the sliced plantains. Cook on one side for about 3 to 6 minutes, or until they start to look golden brown. Flip them over and cook for an additional 3 to 6 minutes, or until golden brown. As the plantains are finished, add them to the bottom of a 9 inch by 13 inch casserole dish. Repeat until all the plantain pieces are cooked and spread out into one even layer in the bottom of the dish.
Spread the sausage over the plantains and then pour the whisked eggs over the sausage. Sprinkle the top with the salt, pepper, and oregano.
Bake the casserole at 350 F for 20 to 25 minutes, or until the center is firm (give it a shake and if it jiggles, it needs more time).
Let the casserole cool for about 5 minutes then slice and serve.