Buns with mushrooms

Ingredients:

Dough

• 0.5 cups whole milk
• 2 and 1/4 teaspoons active dry yeast (7g packet)
• 2 tablespoons of sugar
• 4 tbsp (60 g) butter, melted, plus extra for greasing the bowl and cling film
• 1 large yolk
• 2 and 3/4 cups flour + extra for work
• 1 teaspoon coarse salt

Filling

• 1 small clove of garlic, chopped
• 1 small shallot, chopped
• 1 tbsp fresh thyme leaves
• 220 g of champignons, ends trimmed
• 220 g shiitake mushrooms, stems removed
• 4 tbsp (60 g) butter + extra 2 tbsp, room temperature, for the frying pan
• 1/4 cup dry white wine
• 2 tbsp. heavy cream
• 1/4 tbsp. grated parmesan

Topping

• 4 tbsp (60 g) butter at room temperature
• 1/4 cup chopped parsley
• 2 tbsp. l. grated parmesan

Preparation:

1. Dough: In a medium saucepan, heat the milk and 0.5 cups of water over low heat until the temperature reaches 37°C (but not exceeding 43°C). Remove the saucepan from the heat and stir in the yeast. Sprinkle a pinch of granulated sugar on top and set aside, without stirring, for about 5 minutes until the mixture foams. Then whisk in the butter and egg yolk.
2. In a large bowl, whisk together the flour, remaining granulated sugar, and salt. Make a well in the center and pour the yeast mixture into it, stirring with a wooden spoon until you have a thick, slightly sticky dough. Turn the dough out onto a floured work surface and knead until soft and elastic, about 6 minutes. Form the dough into a ball.
3. Grease the inside of a bowl with butter. Place the dough ball in the bowl, turning it to coat it with butter. Cover the bowl with plastic wrap, draw a circle on the wrap the size of the dough ball, and time it. Let the dough rise in a warm place for about 1.5 hours, until it doubles in size.
4. Remove the dough from the bowl and knead it slightly to release excess air. Form the dough into a ball again and place it in the bowl. Lightly grease a large piece of plastic wrap with butter and place it on top of the dough. Wrap the entire bowl tightly in another piece of plastic wrap and refrigerate for 4 hours or overnight to let the dough rise.
5. Filling: Combine the garlic, shallot, and thyme in a food processor. Add the button and shiitake mushrooms and process until almost pureed (somewhat larger pieces are okay), stopping the processor as needed to scrape down the sides of the bowl. Heat a nonstick skillet over medium heat and melt 4 tablespoons (60 g) butter. Add the mushroom mixture and cook, stirring frequently, until the liquid has released and begins to simmer and brown, 5 to 7 minutes. Reduce the heat to low, add the wine and cream, and bring the mushroom mixture to a simmer. After 1 minute, remove the skillet from the heat and add 1 teaspoon of salt and a few grinds of pepper. Transfer the filling to a medium bowl and let it cool completely. (The filling will firm up a bit, but if it's too warm, you'll have a hard time shaping the buns.)
6. Form the filled buns: Grease a 22 x 32 cm (9 x 13 in) baking pan with 2 tablespoons of softened butter. Turn the dough out onto a floured work surface and press it down. Roll it out into a 25 x 45 cm (10 x 18 in) rectangle, with the long edge facing you. Spread the filling evenly over the dough, leaving about an inch (2.5 cm) from the edge opposite you. Sprinkle the filling evenly with Parmesan cheese. Starting with the side closest to you, roll the dough into a tight log. Lightly brush the empty edge of the dough with water and continue rolling to seal the log. Tuck the ends in slightly, and if the roll appears thicker in some places, smooth it out with your hands.
7. Using a serrated knife, cut the roll into 4-cm-wide rolls, making 12 rolls in total. Place the rolls cut-side down (except the outer pieces) in the prepared pan, spacing them 2.5 cm apart. Cover the rolls with plastic wrap. Let them rise in a warm place until they double in size, leaving no gaps between them, for about 1.5 to 2 hours.
8. Topping: In a small bowl, combine butter, parsley and Parmesan.
9. Position a rack in the center of the oven and preheat the oven to 350°F (175°C). Bake the buns until golden brown and springy when lightly pressed, 25-30 minutes. Spread the topping evenly over the buns, sprinkle with 1 teaspoon of salt, and return to the oven for another 5 minutes to melt the butter and release the aroma. Cool the buns in the pan for 10 minutes and serve.