In a large stock pot, melt 1 1/2 Tbsp. of the butter over medium-high heat. Sautee the onions, carrots, and celery for about 3 minutes. Add the broth, potatoes, and seasonings, and bring to a boil. Reduce the heat to medium, press the veggies down into the broth (making extra sure the potatoes are all covered with liquid), and cover. Cook 15-20 minutes until the potatoes are tender, stirring occasionally. Reduce the heat to low and stir in the peas.
While the soup simmers on low, melt the remaining 4 Tbsp. of butter in a saucepan. Stir in the flour and cook the roux, stirring constantly, for 1 1/2 minutes. While whisking, slowly pour in the milk and whisk quickly to smooth out any lumps. Season with more salt and pepper if you wish, then bring the mixture to a boil (still stirring constantly!) It should be thickening nicely. Once it's boiling, remove from heat, stir in the cream, and then add it to the soup. Stir the soup well to mix all ingredients and incorporate the cream mixture.
Remove the bay leaf, and serve with warm crusty bread.