With your hands, mix the ground chuck, Worcestershire, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper thoroughly in a bowl. Form the meat into 4 patties. Make an indention with your thumb in the center of each patty to keep them from plumping too much when they cook. Refrigerate.
Add the mushrooms to a bowl and toss with the olive oil, 1 teaspoon salt and a pinch of pepper. Grill the mushrooms until tender, 6 to 7 minutes per side. Transfer mushrooms to a sheet pan, lightly cover, and set aside.
Next, remove the sliders from the fridge and place on the grill. Grill the sliders until just cooked through, 3 to 4 minutes per side; top each slider with 2 tablespoons of the cheese 1 to 2 minutes before sliders are done and allow cheese to begin to melt. Remove the sliders from the grill. Drizzle Dijon mustard on inside (gill side) of each Portobello mushroom cap to make "buns." Place each slider on top of a Portobello. Top with 1 lettuce leaf each, 2 slices of tomato and a sprinkle of crispy jalapeños. Place a Portobello "bun on" top of each, gill-side down. Serve and enjoy.