Melt the butter in a heavy-bottomed pan and stir in the flour to make a roux. Stir constantly over low heat until beige and no longer floury tasting, about 30 minutes.
Stir in the vegetables, bacon and parsley. Add the beer, clam juice, bay leaf, seasonings and half-and-half. Stir, cover and simmer 30 to 45 minutes.
Near the end, add the crawfish and serve over rice.