Mill the flour: Start by milling the hard white wheat berries into a fine flour. Measure 4 cups (480 g) for the dough, reserving up to ½ cup if needed.
Prepare the milk mixture: Add ½ cup (120 g) milk, ½ cup (100 g) brown sugar, ½ teaspoon salt, and ½ cup (113 g) butter to a saucepan. Heat over medium heat until steaming and the butter and sugar are melted, stirring occasionally. Do not boil. Remove from heat, add ½ cup (120 g) water, and let the mixture cool to below 110°F.
Mix and rest: Pour the cooled milk mixture into a stand mixer. Add the freshly milled flour and mix until no dry flour remains. Cover and let rest for 10 minutes.
Add yeast and eggs: Add 2½ teaspoons yeast and 2 eggs. Mix until well combined.
Knead: Knead until the dough is soft, smooth, and stretchy, about 5–25 minutes (depending on your mixer). If the dough feels too dry or stiff, add a little milk, 1 tablespoon at a time, until the dough reaches the right consistency.
First rise: Cover and let rise until almost doubled, about 1–2 hours.
Make the filling: Add ½ cup (113 g) very soft butter—softened but not melted—to a medium bowl. Add 1 cup (200 g) brown sugar, a pinch of salt, and 2 tablespoons ground cinnamon. Stir until everything is well combined and forms a smooth, spreadable paste.
Roll and fill: Roll the dough into a 15 × 17-inch rectangle. Spread the filling evenly, leaving about ½ inch along one short edge.
Shape: Roll tightly into a log, starting from the filled edge. Pinch the seam closed and cut into equal rolls.
Second rise: Place the rolls in a parchment-lined pan. Cover and let rise until puffy, about 45–60 minutes.
Bake: Preheat the oven to 375°F. Bake for 20–25 minutes, until lightly golden.
Ice: Add ½ cup (113 g) softened butter, 1 cup (120 g) powdered sugar, ½ teaspoon vanilla extract or vanilla bean paste, and a pinch of salt to a medium bowl. Beat until smooth and fluffy. Add 1 tablespoon (15 g) whole milk and mix until smooth. Add a little more milk, if needed, to reach your desired consistency. Spread the icing over the warm cinnamon rolls and serve.