Proof the yeast by combining warmed milk, yeast, and a teaspoon of sugar in a bowl. Let sit for 10 minutes until frothy.

In a stand mixer, mix the eggs, melted butter, and yeast mixture on low until combined.

Add flour, remaining sugar, and salt. Mix on low, then knead on medium for 5 minutes until dough is smooth.

Transfer dough to a greased bowl, cover, and let rise in a warm place for about 1 hour, until doubled.

Prepare the filling by cooking strawberries, sugar, and lemon juice in a saucepan for 10-15 minutes until thickened. Cool the jam.

Roll out the risen dough into a 14x18 inch rectangle, spread the cooled strawberry jam over the dough, leaving edges bare.

Cut the dough into 2-inch strips, roll each strip tightly, and place them in a greased baking dish, cut side up. Cover and let rise for 30-45 minutes.

Preheat oven to 350°F and bake the rolls for 25-30 minutes until golden brown.

Prepare icing by mixing cream cheese, butter, powdered sugar, and lemon zest until smooth. Add milk for consistency.

Once rolls are baked, let them cool slightly, then drizzle icing over warm rolls.