1. Place eggs in a large saucepan. Cover with water to 1 inch above eggs. Bring just to a boil. Remove from heat; cover and let stand 13 minutes. Drain; cool in ice water 5 minutes. Peel and dice eggs.
2. Cook bacon in a medium nonstick skillet over medium heat until crisp (about 8 minutes). Remove bacon from pan, reserving drippings in pan. Drain bacon on paper towels; crumble bacon, and set aside. Add shallots and garlic to drippings in pan; cook 1 minute, stirring frequently. Remove from heat; add vinegar, oil, and mustard, stirring until combined. Add chicken to pan; toss to coat. Combine mayonnaise and buttermilk in a small bowl, stirring until smooth. Stir in cheese.
3. Working with 1 tortilla at a time, heat tortillas over medium-high heat directly on the eye of a burner for about 15 seconds on each side or until lightly charred. Arrange about 1/4 cup chicken mixture in center of each tortilla; top tacos evenly with lettuce, tomato, and chopped avocado. Divide egg and bacon evenly among tacos, and drizzle evenly with dressing.