Step 1 In the jar of a blender, blend the flour, eggs, milk, salt and melted butter with three-fourths cup water at high speed for 10 seconds, stop and scrape down the sides with a spatula, then blend for 10 seconds more. Strain the batter through a fine-mesh sieve. Cover and let rest, refrigerated, for at least an hour, or overnight.
Step 2 Heat a crepe pan or nonstick saute pan over medium heat until a sprinkle of water sizzles when you throw it on the pan. With a paper towel, spread butter over the pan, being sure to wipe most of it off.
Step 3Using a bowl or a measuring cup with a spout, pour enough batter to just cover the pan (for a crepe pan, a little less than one-fourth cup), immediately swirling the batter around until it covers the whole surface. The batter may be thicker than basic crepes once it has been resting and may need to be thinned a little; if so, add up to one-fourth cup water and stir until blended. It will have a different consistency than sweet crepes (more like honey than pancake batter) and will cook slightly differently, forming bubbles and lacier edges. Adjust the heat, if necessary, to medium-low. As with pancakes, the first one or two galettes are usually experiments.
Step 4When the edges of the galette begin to turn golden and move away from the pan, about 3 minutes, lift the edge nearest to you using a spatula (an offset spatula works best). Flip the galette over. Cook the second side of the galette only long enough for it to set, less than a minute. Remove from the pan and start a stack of galettes, using wax paper to layer between each galette as you cook more. Add more butter when needed with a paper towel.