Step 1

For the rolls: Line 2 baking sheets with parchment paper, then spray with nonstick cooking spray.

Step 2

Combine the flour, sugar, salt and yeast in a stand mixer fitted with a dough hook and stir to combine. With the mixer on low speed, add 1 1/4 to 1 1/2 cups cool water and mix until the dough forms a ball. If the dough is dry and shaggy, add more water, 1 tablespoon at a time, until the dough pulls away from the sides of the bowl. Increase the speed to medium and mix until the dough is smooth and firm, about 10 minutes.

Step 3

Add the dough to a lightly greased large bowl and cover with plastic wrap. Set aside until the dough doubles in size, 1 hour to 1 hour 30 minutes.

Step 4

Preheat the oven to 350 degrees F.

Step 5

Turn the dough out on a lightly floured surface and divide into four equal pieces. Gently form each piece into a ball and set on one of the prepared baking sheets. Cover lightly with plastic wrap and let rest 20 to 25 minutes.

Step 6

Brush the tops of the dough with egg wash and bake until the tops are golden brown, 20 to 25 minutes.

Step 7

Remove to a cooling rack and let cool to room temperature, about 1 hour.

Step 8

Prepare the filling: Meanwhile, combine the cream cheese, sun-dried tomatoes and a pinch of salt and pepper in a bowl, mixing until smooth. Transfer to a plastic sandwich bag. Snip one corner of the bag to create a 1/2-inch hole.

Step 9

Prepare the garlic butter: In a small saucepan, melt the butter, then add the milk, garlic and a pinch of salt. Heat over low heat until the milk is warmed through.

Step 10

In a medium bowl (about 6 inches across the top), whisk the egg and parsley together. While constantly whisking, slowly pour the milk mixture into the egg mixture until combined. Cover to keep warm and set aside. (If the butter starts to solidify, reheat very gently.)

Step 11

Preheat the oven to 400 degrees F.

Step 12

Assemble: Slice into the top of each roll to create 8 equal wedges, being careful to not cut all the way through the bottom. Pipe about an inch of filling between the wedges of each roll. Finish by piping a dollop into the center of each roll.

Step 13

Holding a roll upside-down, dip the entire top into the garlic-butter mixture and place on the second prepared baking sheet, cut-side up. Repeat for each roll. Bake until the rolls are dark golden, 10 to 12 minutes. Let cool for 5 minutes, then serve.