How to Make It
Make the dough: Pour warm milk into the bowl of a stand mixer fitted with the paddle attachment. Stir in sugar and yeast, and let stand until foamy, about 5 minutes. Beat in butter, eggs, lemon zest, and salt at low speed until combined. Switch to the dough hook, add flour, and beat at medium speed until a soft, sticky dough forms, about 5 minutes.
Grease a large bowl with butter. Scrape dough onto a lightly floured surface, and knead a few times. Form dough into a ball, and transfer to the prepared bowl. Cover with plastic wrap, and let stand in a warm place until nearly doubled in size, about 2 hours.
Make the filling: Combine strawberries, sugar, lemon zest, lemon juice, salt, and pepper in a large nonstick skillet over medium-high. Cook, mashing strawberries with a wooden spoon, until the juices start to release, about 5 minutes. Continue to cook, stirring frequently, until mixture is thickened, 3 to 5 more minutes. Let cool completely.
Grease a 9- x 13-inch baking pan with butter. Roll dough to a 10- x 24-inch rectangle on a lightly floured work surface. Spread strawberry mixture evenly over dough, and sprinkle with 1/4 cup chopped pistachios. Tightly roll dough to form a 24-inch-long log. Cut the log crosswise into 12 slices, and arrange slices, cut sides up, in the prepared baking pan. Cover pan with plastic wrap, and let rolls rise in a warm place until they fill the pan, about 2 hours.
Preheat oven to 400°F. Remove plastic wrap from pans, and bake rolls until risen and golden, 20 to 25 minutes. Let cool for 30 minutes.
Make the icing: Whisk together confectioners’ sugar, butter, milk, lemon juice, and salt in a small bowl until mixture is thickened. Drizzle over rolls; garnish with finely chopped pistachios. Serve warm or at room temperature.