Fill a small saucepan with several inches of water and bring to a boil over high heat. Reduce the heat to a rapid simmer and gently add the eggs to the water, one at a time. Cook 6 minutes for a runny yolk. Remove the eggs with a slotted spoon. Run the eggs under cold water and, once cool enough to handle, gently peel.
Working in batches if needed, place the bacon in a single layer in a large frying pan. Fry over medium-low heat until the bacon is crispy on one side. Flip the bacon with tongs and fry until the second side is crispy. Transfer the bacon to a paper towel-lined large plate and repeat frying if needed. Once cool enough to handle, break the bacon into 1-inch pieces.
Place the kale and radicchio in a large bowl and toss to combine. Cover and refrigerate until ready to serve.
When ready to serve, divide the greens among 4 plates. Top with the bacon and croutons. Place 1 egg on each serving and drizzle with the vinaigrette.