Melt the butter in an 8-inch heavy skillet over medium-low heat. When it bubbles, add the flour and salt and stir constantly until the flour begins to brown. Be careful not to let it burn — there will be little color change for the first minute or so, and then the flour will go dark rather quickly.
When the flour-butter mixture is the color of medium-dark toast, turn the heat to low and add the eggs. Stir and turn the eggs until cooked to the desired doneness. Serve immediately, drizzled with the honey if desired.