Preheat the panini grill.
Mix the goat cheese with the ricotta and oregano in a bowl.
Drain the sun-dried tomatoes and chop them coarsely.
Brush the bread slices with olive oil.
Place 2 slices on the work surface, oiled side down, and spread with the cheese mixture.
Add the arugula, sun-dried tomatoes, and parmesan.
Season, then cover with the remaining bread slices.
Grill the paninis for 5 to 10 minutes and serve.