Preheat the oven to 450 degrees . Freeze the meat for 10 minutes.(Chilling raw meat in the freezer firms it up a bit and makes it easier to thinly slice.)
On a foil-lined baking sheet, spray the tomatillos with the vegetable oil; season with salt and pepper. Roast until the tomatillos are charred, about 20 minutes.
While the tomatillos roast, heat 3 tbsp. canola oil in a cast-iron skillet or griddle pan over medium-high heat. Add the onion, garlic, cumin, coriander and oregano; season. Saute until the onions are tender, 10 to 12 minutes. Deglaze with the lager and reduce by half.
Puree the roasted tomatillos in a food processor with the chiles, cilantro and honey. Add the tomatillo puree to the skillet and keep the salsa verde at a simmer.
Shave the meat against the grain. Add 1 tbsp. canola oil to a clean cast-iron skillet or griddle pan over high heat. Sear and toss the meat to cook through, working in a few batches. Season and, once all the meat is browned, dress with worcestershire.
Turn on the broiler. Pile the meat on the roll bottoms, scatter cheese on top and arrange on a baking sheet. Broil for 1 minute to melt cheese. Before serving, add lots of salsa verde and the bun tops.