Make the dough. In a large bowl, whisk 3 1/2 cups flour, yeast, sugar, and salt. Add warm milk, egg, melted butter, and vanilla. Stir with a wooden spoon until a shaggy dough forms. If it’s very sticky, add more flour a tablespoon at a time. You’re aiming for soft and slightly tacky, not wet.
Knead. Turn the dough onto a lightly floured surface. Knead 6 to 8 minutes until smooth and elastic. You can use a stand mixer with a dough hook on medium-low for about 5 minutes. If the dough sticks to your hands like gum, dust with a bit more flour, but avoid overdoing it. Soft dough makes soft rolls.
First rise. Place dough in a lightly oiled bowl, cover with a clean towel or plastic wrap, and let rise in a warm, draft-free spot until doubled, about 60 to 90 minutes. I like the oven with the light on. Cozy and consistent.
Prep the filling. Toss the diced strawberries with cornstarch, lemon zest, and a pinch of salt. In a separate small bowl, mix the brown sugar and cinnamon. Have your softened butter ready. This little step keeps the berries from leaking too much juice while they bake.
Roll it out. Punch down the dough. Roll into a 12 by 16 inch rectangle on a lightly floured counter. Spread the soft butter all over, right to the edges. Sprinkle the cinnamon sugar evenly, leaving a small 1/2 inch border along one long side so the seam seals.
Add the strawberries. Scatter the berries evenly over the sugar. If they look super juicy, dab once with a paper towel. No need to be fussy. A little juice is flavor.
Roll and chill briefly. Starting from the long side opposite your clean border, roll up fairly tight. Pinch the seam to seal. If the roll feels soft or slippery from berry juice, pop it onto a tray and chill 10 to 15 minutes. This makes slicing neat and easy.
Slice. Use unflavored dental floss or a very sharp knife to cut 12 even rolls. Floss trick: slide under the log, cross the ends over the top, pull tight. Clean cuts, no smooshing.
Second rise. Arrange the rolls in a parchment-lined or greased 9x13 pan with a little space between them. Cover loosely and let rise until puffy, about 30 to 45 minutes. Meanwhile, preheat the oven to 350°F or 175°C.
Bake. Bake 22 to 26 minutes, until lightly golden and the centers of the middle rolls no longer look doughy. If they brown too fast, tent with foil for the last 5 minutes. The berries will bubble and smell like warm jam. So good.
Glaze. Beat the cream cheese until smooth. Add powdered sugar, jam or puree, vanilla, and a pinch of salt. Thin with milk to your favorite consistency, thick or drippy. Spread over warm rolls. The glaze melts into the swirls a bit and makes everything glossy and pink.
Serve. Let the pan sit 10 minutes so the filling settles. Then pull apart a roll, admire those strawberry freckles, and enjoy while cozy-warm.