In a small bowl, thoroughly whisk together jelly and mustard. Spread a thin, even layer of the jelly mixture over each crepe. Fold the crepes in half to form a semicircle with the jelly sandwiched inside. Top each folded crepe with a slice of each cheese and then layer 3 slices of ham on top of the cheese. If the rounded edge of the crepe is sticking out, fold it inward and tuck under the cheese then roll the crepe up tightly and set seam-side down. Repeat for remaining crepes.
Heat 2 tablespoons of butter in a large skillet over medium heat. In a large bowl, whisk together milk, eggs, and vanilla extract. Whisk in a generous pinch of kosher salt. Using tongs, briefly dip a crepe into the egg mixture. Allow excess to drip off and transfer to the skillet, seam-side down. Repeat with another crepe. Fry crepes until golden all over, turning occasionally, about 2 minutes per side. Transfer to a plate. Repeat with the remaining crepes, frying two at a time and adding butter as needed.
Dust crepes with powdered sugar. Serve warm with berries and the remaining jelly-mustard mixture.