Heat the vegetable oil in a skillet set over medium-high heat. Once the oil is hot, add the peppers and cook, turning occasionally, until blistered on all sides, about 5 minutes.
Transfer the peppers to a cutting board. Once they are cool enough to handle, slice off and discard the stems, then transfer the peppers to the bowl of a food processor.
Add the parsley, cilantro, oregano, shallot, garlic, vinegar, lime juice, honey, salt, and pepper to the food processor and pulse until roughly chopped. With the motor running, stream in the olive oil. Continue blending until combined, scraping down the sides as needed. Taste and season the chimichurri with salt and pepper, then set aside.
Preheat a grill or heat a stovetop grill pan over medium-high heat. If using a grill, lightly oil the grate.
Season the steak generously with salt and pepper. Place the steak on the grill and cook undisturbed for 6 minutes. Flip it once and continue cooking until it reaches your desired level of doneness. For medium-rare, cook the steak until it reaches an internal temperature of 130 degrees F.
Transfer the steak to a cutting board, cover loosely with foil, and let rest for 10 minutes.
Slice the steak against the grain into thin strips. Top the steak with chimichurri and serve.