In a small bowl, mix together the mayonnaise, mustard, garlic, and rosemary. Add a little salt to taste. Set aside for up to 30 minutes at room temperature or up to 1 day refrigerated.
To assemble, place the bottom half of each croissant on your work surface, cut side up. Spread 2 tablespoons of the aioli on each croissant half, followed by the sun-dried tomatoes. Lay the Brie slices on top, followed by the Swiss cheese and turkey. Top with the remaining croissant halves, cut side down.
To grill, heat a large nonstick skillet over medium-low heat for 2 minutes. Put the sandwiches into the pan, cover and cook for 2-3 minutes, until golden brown. Carefully turn the sandwiches, pressing each one with a spatula to compress the bread and filling. Cover and cook for 2 to 3 more minutes, until the undersides are golden brown. Turn the sandwiches once more, press with the spatula again, and cook for 1 minute. Remove from the pan. Let cool for 5 minutes. Cut in half and serve.