Make the dipping sauce: In a bowl, whisk together sauce ingredients until fully combined - including Thai sweet chili sauce, barbecue sauce, teriyaki sauce, soy sauce, Worcestershire sauce, and optional fish sauce. Set aside. The sauce can be made ahead and stored in the fridge for up to one week.
Make the cream cheese filling: In a large bowl, combine cream cheese, thinly sliced green onions, soy sauce, Worcestershire sauce, sugar, and chili crisp (or crunchy garlic chili oil), and optional fish sauce. Mix until everything is fully incorporated.
Heat the oil: Heat neutral oil for frying (vegetable or canola) in a heavy-bottomed pot or Dutch oven over medium-high heat until it reaches 350°F. Use a thermometer - maintaining oil temperature is the key to crispy egg rolls.
Roll the egg rolls: While the oil is heating, wrap the egg rolls. Lay one egg roll wrapper flat in a diamond orientation with a corner pointing toward you. Spread about 2½ tablespoons of cream cheese filling towards the bottom third of the egg roll wrapper (closest to you), leaving about 1/2" of space on the outer edge. Top with about 3 tablespoons of chopped brisket - don't overfill or the wrapper won't seal. Dip your finger or a pastry brush in a small cup of water, and moisten the entire outer edge of the egg roll wrapper. Fold the bottom corner up over the filling, tuck in the two side corners, then roll up toward the top corner. Dab the top corner with a bit more water, if needed to seal. Repeat with remaining wrappers and filling.
Fry the egg rolls: Working in batches of 4–5 egg rolls (never overcrowd the pan), carefully lower the egg rolls into the hot oil. Fry for 4-6 minutes, turning occasionally, until deep golden brown and crispy all over. Transfer to a wire rack or paper towel-lined plate to drain.
Serve: Serve immediately with the Asian BBQ dipping sauce on the side. These are best hot and fresh.