For the marinade:
1/2 cup balsamic vinegar
2 tablespoons Dijon mustard
2 garlic cloves, peeled and sliced
1 cup extra-virgin olive oil
1 teaspoon kosher salt
Freshly ground black pepper
1 (2- to 3-pound) flank steak
For the stuffing:
3 ounces prosciutto
6 slices provolone cheese
1 cup spinach, basil, or arugula
Kosher salt and pepper
Neutral cooking oil, such as canola
For the marinade, combine balsamic vinegar, Dijon, and garlic in a blender and puree until smooth. With the machine running, slowly pour in the oil until thick and creamy. Season with salt and pepper.
Transfer the mixture to a plastic zip-top bag (or vacuum seal) and add the flank steak. Remove excess air and refrigerate, turning occasionally, for a minimum of 4 hours and up to 24 hours.
Remove the flank steak from the marinade and pat dry, discarding the marinade. Arrange the steak on a clean work surface so the long edge runs perpendicular to you. Using a sharp knife and cutting parallel to your work surface, butterfly the steak in half lengthwise. Make sure not to cut all the way through. (Leave a 1/2- to 1/4-inch portion along the edge.) Fold open the meat like you would a book and gently flatten the seam to form a rectangle. Using a meat mallet or rolling pin, pound the steak to a 1/4-inch thickness.
Arrange the meat on a work surface with the grain running north and south. (You want to roll the steak this way so that when it is cut, you slice it perpendicular to the grain.) Lightly season the top with salt and pepper. Lay the prosciutto slices in an even layer parallel to the grain, leaving a one-inch space at the top edge. Next add the provolone, followed by the spinach.
Start rolling the flank steak away from you (south to north), making sure to keep it as compact as possible as you roll. Once rolled, tie the stuffed roll in regular intervals with kitchen twine and season the outside with salt and pepper. (At this point the rolled flank steak can be refrigerated for up to two days.)
To cook the steak the oven: Preheat oven to 350°F. Add a few tablespoons oil to a large cast iron or oven-proof skillet and heat on medium-high to high until smoking. Add the rolled flank steak to the pan and sear until deep golden brown on all sides, 8 to 10 minutes. Transfer the skillet to the oven and continue cooking until an instant-read thermometer reads 125°F in the middle of the roll, 8 to 10 minutes. Transfer the steak to a cutting board and tent loosely with aluminum foil. Allow to rest for 10 to 15 minutes before slicing. Snip the strings and cut steak into 1/2 to 3/4-inch slices.
To cook the steak on the grill: Place a large cast iron skillet in the grill, cl