Add sliced peppers and onions to the hot oil. Cook, tossing frequently (tongs work great for this), until the peppers and onions begin to soften.
Add taco seasoning packet to pepper mixture and toss well to coat. Do not add water.
Cook for an additional 2-4 minutes, until the <g class="gr_ gr_260 gr-alert gr_gramm gr_inline_cards gr_run_anim Punctuation only-ins replaceWithoutSep" id="260" data-gr-id="260">vegetables</g> reach desired level of softness.
Meanwhile, cook the burgers on a grill on high heat or in a skillet on the stove over high heat. Burgers should cook for approximately 3-6 minutes per side until the internal temperature measures 160 degrees Fahrenheit with a meat thermometer.
Toast hamburger buns, if desired.
Place one cooked hamburger on each bottom bun. Top with 1 slice of pepper jack cheese and a generous portion of the pepper mixture. Finish with the top half of the bun.