In a large nonstick skillet, heat oil over medium heat; add bacon. Cook, stirring frequently, until crisp, about 5-7 minutes; drain bacon on paper towels and set aside.
Reduce heat to medium-low; add onion and mushrooms. Cook, stirring frequently, until softened, about 2-3 minutes.
Remove skillet from heat; stir in vinegar, mustard and sugar. Add bacon and gently stir; spoon over kale and toss well. Allow salad to sit for 5 minutes; add eggs and serve.