- In a small saucepan, heat milk, water, and butter until butter is completely melted. Stir to combine and transfer to your stand mixer bowl. Let sit until temperature cools to 110°F. 
- Stir in yeast and honey. Let stand for 10 minutes or until yeast mixture is bubbly. 
- While mixture is resting, sift flours together in a medium bowl. 
- Turn on stand mixer, fitted with a dough hook, and add salt, egg, and egg white. With mixer still on, add your flour mixture, about a 1/2 cup at a time, until a shaggy dough forms. 
- Knead dough in stand mixer for 3 to 4 minutes on medium speed until dough pulls away from bowl and is soft and elastic. 
- Place dough in an oiled bowl. Cover with plastic wrap or clean towel, and let rest for one hour at room temperature. 
- Preheat oven to 400°F. Grease a 9-inch round pan or skillet thoroughly. 
- Punch down dough and turn out onto clean surface. Divide into 8 or 9 equal-sized pieces. 
- Cut goat cheese into 8 or 9 pieces. 
- Pat each piece of dough flat with the palms of your hands and place a piece of goat cheese in the center. Wrap edges of dough around cheese, and form a ball with the dough, leaving the goat cheese in the center. Place rolls in prepared pan. 
- Prepare egg wash: Whisk extra yolk with a teaspoon of water. Brush a bit on top of each roll. 
- Press a walnut in the center of each ball, if desired. 
- Bake for 25 to 30 minutes, or until golden brown. Serve immediately for a melty, delicious warm bun. 
- The rolls can keep for up to two days in an airtight container. Reheat in microwave or wrap in foil to reheat in oven before serving.