Beat butter and cream cheese until well mixed and soft. Slowly add flour. Once all flour is added, turn out and knead until well incorporated and smooth. Form a disk, wrap tightly in plastic wrap, and refrigerate for about 30 mins.

In food processor (or by hand, ew) chop mushrooms, onion, and garlic together, until mushrooms and onions are small, fairly uniform sized bits. Put in frying pan with olive oil, and cook down until mushrooms are very soft – almost mushy. Add thyme and sea salt, remove from heat, and stir in the ¼ cup cheese. Put aside and allow to cool a bit.

Preheat oven to 450.

Roll chilled dough out to about ¼″ thick. Use a large glass or cookie cutter (about 3-4″ in diameter) to cut out rounds.

Put a scant tablespoon of filling in the center of each round, along with a strip of cheese. Whisk the egg and water in a mug, brush a small amount along ½ the edge of each round. Seal, using the egg mix like a glue. Arrange turnovers onto a baking sheet, pressing down firmly around the edges to seal completely.

Brush the tops of turnovers with egg wash, then pierce each with a fork a few times. Bake for 10-12 minutes, until golden.