01 -
Crack eggs into a bowl, add whole milk, salt, and black pepper; whisk until blended and slightly frothy.
02 -
Heat olive oil in a large skillet over medium heat until shimmering; add onions and red bell peppers and cook, stirring frequently, until softened and lightly golden, approximately 4 to 6 minutes.
03 -
Add sliced smoked chicken and apple sausage to the center of the pan; cook until browned on both sides and heated through, about 4 to 5 minutes; toss vegetables to glaze sausage with their oils.
04 -
Reduce heat to medium-low, push sausage and vegetables aside, pour eggs into the open space; let sit briefly then gently stir with spatula until small curds form and eggs are just set and glossy, 2 to 3 minutes; remove from heat to finish cooking with residual heat.
05 -
Warm each tortilla over a low gas flame or in a dry skillet for 10 to 15 seconds per side until pliable and lightly blistered; stack tortillas and keep covered with a clean towel to maintain softness.
06 -
Place tortilla on a clean surface, sprinkle shredded cheddar cheese down the center, add a scoop of egg-sausage-vegetable mixture; fold sides inward, pull bottom edge up over filling, then roll tightly to enclose.
07 -
Place burritos seam-side down in a dry skillet over medium heat; cook 1 to 2 minutes per side until tortilla crisps lightly and cheese melts, sealing the wrap.
08 -
Open burrito slightly or serve open-faced and top with shredded lettuce, diced tomatoes, and chopped cilantro; squeeze fresh lime over before eating for brightness.