In a blender, combine the flour, half-and-half, salt, eggs and 2 tablespoons of the melted butter and pulse for 10 seconds. Pour the batter into a sieve set over a bowl. With a rubber spatula, push the batter through the sieve into the bowl. Add the soda water to the batter and gently mix until fully incorporated. Cover the bowl with plastic wrap and refrigerate for at least 1 hour. (The batter will keep in the refrigerator for up to 48 hours.)
Preheat the oven to 200 degrees F.
Heat a 10-inch nonstick skillet over medium-high heat. With a pastry brush, grease the skillet with some of the remaining butter. Scoop 1/4 cup of the batter onto the skillet, swirling the batter to create an even surface. Add a little more batter if needed. Cook the crepe until light brown on the bottom, about 2 minutes. Flip the crepe with a spatula and cook for 1 more minute. Transfer the crepe to a plate and keep warm in the oven until serving (put a sheet of parchment paper between each crepe). Wipe out the skillet with a paper towel, then brush with more butter and repeat with the remaining crepe batter.