Preheat oven to 350ºF (180ºF).
In a large bowl, whisk 3.5 cups whole grain rye flour with 1/4 cup sugar, 2 teaspoons baking powder and 1/2 teaspoon salt.
Add 8 tablespoons melted butter, 1 cup rye starter, 1/4 cup water and 1 large egg.
Mix everything, at first with a spoon, then your hand until dough comes together (If you have a mixer with a dough hook, it's easier to mix). The dough will be sticky. To manage the stickiness, generously sprinkle work surface with rye flour and transfer the dough onto it. Sprinkle more flour on top and knead some more.
Separate the dough into 8 pieces, form into balls, and flatten them with your hand to about the size of your palm.
Score the cakes with a sharp knife. Transfer to parchment lined cookie sheet.
Whisk 1 small egg with 1 tablespoon of sugar, and brush the tops of the rye cakes.
Bake for 20-25 minutes, until the top start to brown slightly. Less baking time will produce softer cakes, more time - crunchier.