Combine warm water and milk in a bowl of a stand mixer fitted with paddle attachment.

Sprinkle yeast over and stir to moisten evenly. Let stand until yeast dissolves, stirring occasionally, about 8 minutes.

In a medium bowl, combine flour and salt. Add to the yeast mixture. Blend at medium-low speed until shaggy lumps form, scraping down sides of bowl occasionally, 1 to 2 minutes.

Add eggs one at a time beating until blended after each addition.

Beat in sugar. Increase mixer speed to medium and beat until dough is smooth, about 3 minutes.

Reduce speed to low and add butter, one tablespoon at a time, until blended after each addition. This will take 4-5 minutes. Dough will be soft and silky.

Increase speed to medium-high and beat until dough pulls away from sides of bowl and gathers around the paddle, about 3 minutes.

Lightly butter a large bowl. Scrape dough into bowl. Cover with plastic wrap and let dough rise in a warm, draft-free area until almost doubled in volume, 1 hour 30 minutes to 2 hours.

Butter or line 12 muffin cups, every other one on two standard muffin pans.

Roll out dough on a lightly floured surface to a 9 x 12-inch rectangle and about ½-inch thick.

Spread cheese and prosciutto evenly over the dough and press slightly to adhere.

From the long edge, fold the dough into thirds (like you’re mailing a letter). Roll gently again to about a 5 x 13-inch rectangle. Trim the ends if needed and cut into 12 1-inch strips.

Cut each strip into thirds. Roll each piece between palms into ball.

Place 3 balls in each prepared cup. The dough will fill cup.

Place muffin pan in warm draft-free area covered with plastic wrap or parchment that allows room for dough to rise. Let dough rise until nearly doubled, 50 to 60 minutes. It will be an inch or so above the muffin pan.

Preheat oven to 400°F and position rack in the center.

Brush egg wash over risen dough. Bake brioches until golden brown, covering with foil if browning too quickly, 16-18 minutes.

Transfer pans to cooling racks. Let stand 10 minutes. Carefully remove brioches from pan. Serve warm or at room temperature. Enjoy!