For the marinade: Whisk the soy sauce, lime juice, honey, cumin, cayenne, garlic and some salt and pepper in a bowl. Place the steak in a large freezer bag or a baking dish and pour the marinade over it. Marinate the steak at least 30 minutes and up to 3 hours in the refrigerator.
For the chimichurri: Whisk together the oil, red wine vinegar, lime juice, garlic, jalapeno and red onions. Add the herbs and toss to combine. Set aside until ready to build the sandwich.
Heat a grill pan to high heat.
Remove the meat from the marinade, let any excess drip from the meat so it is not overly wet. Grill the meat for 4 to 6 minutes each side for medium-rare. Transfer the meat to a cutting board, tent with foil and let rest for 5 to 10 minutes.
While the meat rests, toss the peppers and onions in a bowl with the oil and salt and pepper. Place onto the grill and cook until the vegetables are nice and charred, 6 to 8 minutes.
Cut the pita pockets in half.
Slice the rested skirt steak into thin strips against the grain.
To build the pocket: Lay a piece of Havarti cheese in the pita, add slices of skirt steak, some peppers and onions and pour in some chimichurri.