Mix flour, eggs, salt, and water by hand with a wooden spoon or using a mixer until combined. Let rest for 10 minutes.
Bring a large pot of salted water to a boil, filling it to about 2 cm (0.8 inches) below the rim. Add the spaetzle dough in portions using a spaetzle maker, press, or scraper. When the spaetzle float to the surface, they are cooked. Remove each batch with a slotted spoon and drain in a colander.
Peel, core, and cut the apples into small pieces.
Heat the butter in a pan over medium heat. Add the apple pieces and sear for about 2 minutes, then reduce heat to medium-low. Cook until the apples are soft and tender, about 5-10 minutes, stirring occasionally.
Add the cooked spaetzle to the pan with the apples and toss gently. Heat for about 1-2 minutes until warmed through.
Sprinkle sugar over the apple spaetzle. If desired, increase heat to medium and cook for about 1-2 minutes while stirring gently to caramelize the sugar. Serve with cinnamon sugar available to sprinkle on top.