Trim excess fat from the steak and slice against the grain into strips just under 1 inch wide; rotate the strips and cut into bite-size pieces.
In a large bowl whisk together 4 tablespoons soy sauce, 2 tablespoons honey, 1 tablespoon chili sauce, 1/2 teaspoon sesame oil, and 1 tablespoon minced garlic.
Add the steak pieces to the marinade and toss to coat; cover and marinate at least 20 minutes and up to 4 hours.
While the steak marinates, make the dipping sauce: zest 1 lime to get 1/2 teaspoon zest and juice both limes (about 3–4 tablespoons), then combine the zest and juice with 1/2 cup mayo, 3 teaspoons sriracha, and 1 teaspoon sugar; season with salt and pepper to taste and stir well.
Heat a large nonstick skillet over medium-high to high heat and add 1 tablespoon sesame oil; the pan should be very hot so meat sizzles on contact.
Cook the steak in a single layer without crowding; let pieces sear undisturbed for 30–45 seconds, flip and cook another 30–45 seconds to sear the outside but keep the interior tender.
Transfer cooked bites to a plate, add remaining sesame oil to the pan, and repeat with remaining steak in batches.
When all steak is cooked, sprinkle with toasted sesame seeds if desired and serve immediately with the prepared dipping sauce.