Fill a wide pot with water (at least 6 inches) and bring the water to a boil. As the water is heating, make the scratch egg drop noodles. Combine the paleo flour and salt in a large mixing bowl. Use a fork to mix an egg into the flour until you have a shaggy dough.
One tablespoon at a time, stir cold water into the dough. You may not need to use all the water to complete the dough, or you may need to use a little more. To test if the dough is the right consistency, lift the fork and look for a slow, natural sagging in the dough until it falls off the fork. If it’s falling off in large clumps, or not falling off at all, add more water to the dough. If the dough doesn’t stick to the fork at all and looks like a liquid, the dough is too thin.
When the water is at a rolling boil, place a spaetzle maker over the pot. This can be a rectangular tray with holes and a sliding tool to pull the dough or a wide, circular plate with holes to press the dough through. Place about 1 cup of dough into the spaetzle maker and slide/press the noodles into the boiling water. The noodles will rise almost immediately.
Let the noodles cook in the boiling water for just about 10 seconds. Use a slotted spoon to transfer the noodles to a serving bowl, leaving behind any excess liquid. Repeat Steps 3 and 4 until all the noodles are cooked. Melt the butter in the microwave and pour it over the noodles. Stir the noodles until they’re lubricated with the butter and serve warm.