In a large, heavy skillet over medium high heat, fry the bacon until crisp, about 10 minutes. Remove the bacon and leave the fat in the skillet.
Then place the potatoes, broccoli, celery, carrots, and onion in the bacon fat, reduce heat to medium and saute for 5 minutes. Place the kielbasa over all, to allow the juices to trickle down over the vegetables.
Saute for 5 to 10 more minutes, or to desired tenderness on the vegetables. Season with salt and pepper to taste, crumble the reserved bacon and return it to the skillet, and stir to combine.