Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 25 minutes. Drain potatoes and mash; season with salt and pepper.
Combine flour and 1 teaspoon salt in a large bowl while potatoes are cooking. Stir sour cream and baking soda together in a second bowl. Add water to flour mixture and blend in, followed by sour cream mixture. Knead into a smooth dough, cover with plastic wrap, and refrigerate for 10 to 15 minutes.
Melt butter in a skillet over medium heat and cook onions until browned, 5 to 10 minutes. Add mushrooms and cook until browned, about 5 minutes. Add to mashed potatoes.
Divide dough into 4 portions and roll each portion into a 1 1/2-inch thick rope. Cut ropes into small 1/2-inch pieces. Press each dough piece into a small flat circle and place 1 teaspoon of potato filling in the center. Fold dough over into a half-moon shape and seal edges.
Bring a large pot of salted water to a gentle boil. Add the vareniki in batches and cook until they float to the surface, about 3 minutes. Cook for 2 to 3 minutes more. Remove with a slotted spoon and place in a colander to drain.