Make the cilantro lime dressing. In a blender or large jar or container if using an immersion blender, place the egg and slowly blend in the olive oil until it emulsifies and thickens. Add the rest of the ingredients and blend until thoroughly combined. Cover and refrigerate to allow the dressing to thicken before use.
Make the jammy eggs. Bring 2 quarts of water to a gentle boil over medium-high heat and add salt. Carefully add the eggs to the water and cook for 7 1/2 – 8 minutes, adjusting the heat as necessary to prevent the water from boiling too rapidly and cracking the eggs.
Meanwhile, prepare an ice water bath. When the eggs are done, immediately remove them to the ice water with a slotted spoon and let them cool before peeling. Cut each egg in half lengthwise and set aside.
While the eggs are cooking, saute the corn. Add the butter and corn to a large saute pan over medium-high heat and saute for a few minutes until warmed through. Season with a pinch of salt and freshly ground black pepper. Set aside.
Assemble the salad jars or bowls. In a medium bowl, toss the shredded cabbage with a few spoonfuls of the cilantro-lime dressing. Divide the cabbage among four jars or bowls and top with a couple spoonfuls of the sauteed corn and some chicken breast. Spoon some black beans into the jars along with a forkful of marinated red onions. Add a quarter of the cubed cheese and a few broken tortilla chips, and top the jars with 2 egg halves and a handful of cherry tomatoes. Enjoy now or close the jar and keep in the fridge to eat later!