Mix soft butter, sour cream, sugar, egg, vanilla and salt with a whisk or mixer until homogeneous.
Mix flour with baking powder.
Add the dry flour mixture in batches to the liquid sour cream mixture and knead it briefly and briskly to form a very soft dough. Divide the dough into four equal pieces and refrigerate them, wrapped in an airtight container, for 1 hour.
First, get one piece of dough out of the refrigerator, divide it into small pieces, and shape each piece into a ball. Spread the balls with plenty of space between them on a baking sheet lined with baking paper, flatten them just slightly and bake the "mushroom hats" in a preheated oven at 180 °C top and bottom heat for about 10 - 15 minutes, depending on the size of your cookies. Repeat the same with the second piece of dough from the refrigerator.
Let the "mushroom hats" cool a bit and, while they are still warm, carefully cut out a small hollow in the center of each "mushroom hat" from the flat side using a knife. Let the "mushroom hats" cool completely afterwards.
Get the third piece of dough out of the fridge, divide it into small pieces as well, and shape each piece of dough into a "mushroom stem". Then cut each "mushroom stem" lengthwise into two equal halves and spread the "mushroom stem" halves flat side down on a baking sheet lined with parchment paper.
Bake the "mushroom stem" halves in a preheated oven at 180 °C top and bottom heat for about 10 - 15 minutes, also depending on the size of your cookies, and let them cool.
Repeat the last two steps with the last piece of dough you still have in the fridge.