In a large skillet over medium heat, heat olive oil and swirl pan to evenly coat. Add onions and cook over medium heat, stirring occasionally until onions are a deep golden brown, about 20 minutes.
In a food processor, combine dried cranberries and mustard. Pulse several times until a paste forms. Spread inside of 2 bread slices with cranberry mustard. Spread outside of bread slices with softened butter.
Begin layering spinach, turkey slices, caramelized onions, and brie cheese on top of cranberry mustard. Add top piece of bread butter-side facing up.
Heat a panini press or large skillet over medium-high heat. Cook the sandwiches one at a time in panini press or in skillet until cheese is melted and bread is golden brown, about 3-5 minutes. (flip paninis once if using skillet) Cut sandwiches in half and serve immediately while warm. Enjoy!