For the vegetable filling

1. Melt butter in a large heavy skillet over medium-low heat. Remove from heat, add garlic, and sauté until garlic is fragrant (about 30 seconds). Add rosemary, carrots, bell pepper and zucchini. Toss until vegetables are evenly coated in butter. Set aside.

For the steak rolls

1. Be sure to have several 12-inch long pieces of butcher’s twine ready to tie up the steak roll (see Notes).
2. First, butterfly the skirt steak by laying it flat on a work surface. Using a long-bladed slicing knife, cut the steak horizontally (parallel to the counter top) almost in half lengthwise, taking care not to cut all the way through or to make holes in the meat. Open the meat like a book to lie flat. Using a meat mallet, pound steak until it is an even thickness throughout and about 1/3 inch thick.
3. Season both sides of the steak with salt and pepper.
4. With steak laying open and flat, turn the steak so that the grain is running left to right. Sprinkle Parmesan cheese evenly over the steak, leaving a 1/2 inch border. Gently press down on the cheese to help it stay in place. Arrange vegetable mixture evenly on top of the cheese so the julienne strips lay parallel to the grain of the steak. Set pan aside but do not wash it out.
5. Roll up the steak jelly-roll fashion. You should be rolling the steak parallel to the direction of the grain. Tie a piece of twine around the middle of the roll. Working from the inside out, continue tying the roll every 1 1/4 inches, pushing any vegetables back in that have fallen out and tightening up the roll as you go.
6. With a sharp knife, cut the roll into slices between each of the tied pieces of twine.
7. Heat oven to 375 degrees. Line a rimmed baking sheet with aluminum foil.
8. Wipe out the skillet used earlier for the vegetables with a paper towel. Add 1 tablespoon oil to the skillet and heat oil over medium-high heat until it begins to shimmer. Add about half of the steak rolls, cut side down and sear for 1-2 minutes. Turn steak rolls over and sear on second side, adding more oil as needed. Put seared steak rolls on prepared baking sheet. Repeat with second half of steak rolls.
9. Place the steak rolls in oven and roast for 10 minutes for medium rare. Let rest 5 minutes before serving. While the steak rolls are roasting and resting, make the balsamic glaze.

For the balsamic glaze

1. Melt the butter in a small saucepan over medium heat. Add shallots and sauté until they turn soft and translucent, 1-2 minutes.
2. Add the balsamic vinegar, brown sugar and beef stock and stir to mix evenly.
3. Bring the sauce to a boil, reduce heat and let the sauce simmer until it is reduced to almost half and thickens slightly.
4. Remove twine from steak roll and serve with balsamic glaze.