In the pan you plan to cook the soup in, fry the bacon on both sides until most of the fat is rendered, but not crispy.

Remove the bacon from the pot, leaving the rendered grease behind.  Add the carrots, celery, and onion.  Cook over medium heat, stirring to get up all the bacon-y goodness, until the vegetables are softened, 5-7 minutes.

Add the beans, broth, water, and bay leaves.  Partially cover and cook over low heat for a good long while.  (I let it go for a couple of hours- this is a great thing to do on a rainy sunday, because it makes your kitchen smell fantastic.  But I think 30 minutes would do in a pinch.)

Chop the bacon in to tiny pieces.  Add chopped bacon and tomato paste to the soup.  Cover again and cook another 20 minutes or so.

Just before serving, use an immersion blender to half-puree the soup, leaving some whole beans and chunks intact.  (If you don't have an immersion blender, remove about 2 cups of the soup, puree in a blender, and stir back into the pot.)  Season with salt and pepper to taste (it shouldn't need much; the bacon is salty, so start with a light hand) and serve.