Preheat the oven to 425F. Line two quarter sheet pans with parchment (see note). Lightly grease one of them with olive oil.
If making turkey breakfast sausage, in a medium-large bowl, add all the ingredients and use your hands to mix thoroughly so that the spices, etc…get evenly distributed.
Transfer to the greased baking sheet and press into an even, compact layer that should take up the whole ¼ sheet pan or half of a regular sheet pan (you’ll be cutting it into 8 pieces). Drizzle the top with some extra olive oil (this can help it brown a little on top).
In the same medium-large bowl, whisk together the eggs and salt.
Pour the eggs into the other baking sheet. Carefully transfer the eggs and sausage to the oven.
Bake the eggs for 10-12 minutes (or until eggs are just cooked) and the sausage for 10-15 minutes, or until the sausage is cooked through. If you want it to brown on top, bake for just 10 minutes and broil it on high for a minute or two at the end. Cut the egg and sausage into 8 rectangles.
To make the sauce (if using), in a small bowl, mix together the ketchup and mustard.