How to Make It
In the bowl of a stand mixer, whisk together by hand the warm milk, yeast, and sugar. Set aside until foamy, about 5 minutes.
Whisk in the egg and canola oil. Add the flour and salt. Using a dough hook, mix on low speed until the flour is incorporated. Increase the speed to medium-low and knead until smooth, about 8 minutes.
Lightly flour a work surface, turn out the dough, and knead into a smooth ball. Place the dough in a clean, lightly oiled bowl. Cover with plastic wrap and let rise at room temperature until doubled in size, 1 to 1 ½ hours.
Lightly flour a work surface and turn the dough out. Divide into 12 to 14 equal-size pieces (weighing approximately 2 ounces each) and roll each into a smooth ball. Cover with plastic wrap and let rest for 30 minutes.
Combine the feta and parsley in a small bowl.
Line a baking sheet with parchment paper. Lightly flour a work surface.
Roll each ball into a 5-inch circle. Cut four slits, each about 1 ½ inches long, starting from the edges and going toward the center at the north, south, east, and west ends of the balls. Place a generous tablespoon of the feta and parsley mixture in the center of the dough. Starting at the top, fold that quarter of the dough over the cheese. The dough will partially cover but not enclose the cheese. Fold about ¼ inch of the dough edge back to form an open petal. Fold the dough quarter at the bottom over the cheese and fold back the top to form an open petal. Fold the right side over the cheese, folding back to form a petal. When folding the final quarter over, tuck the edges underneath the rose, folding back that piece to form a petal. Place on the prepared baking sheet. Repeat with the remaining balls of dough, leaving two inches in between the rolls.
Cover with plastic wrap and let rise at room temperature until almost doubled, 30 to 45 minutes.
Preheat the oven to 350°F.
Whisk together the eggs and milk to make an egg wash. Brush the rolls with the egg wash, then bake until golden brown, 25 to 30 minutes. Rolls can be served warm or at room temperature, and are best eaten the day they are made.