Warm 1 cup of whole milk to between 105°F and 110°F. Combine with 2 tablespoons of sugar and 2 teaspoons of active dry yeast. Stir and let sit for about 10 minutes until frothy.

In a stand mixer, whisk together 2 large eggs and 1/4 cup of melted unsalted butter. Add the yeast mixture and mix well. Gradually incorporate 4 cups of all-purpose flour, 1/4 cup of sugar, and 1 teaspoon of salt. Mix on low, then knead on medium speed for 5 minutes.

Transfer the dough to a greased bowl, cover with a kitchen towel, and let rise in a warm spot for about 1 hour until doubled in size.

Prepare the strawberry jam by cooking 2 cups of fresh strawberries with 1/2 cup of sugar and the juice of 1 lemon over medium heat, mashing slightly.

Thicken the jam by stirring together 1 tablespoon of cornstarch and 1 tablespoon of water, then adding to the simmering mixture until thickened.

Roll out the dough into a rectangle about 14x18 inches and spread chilled strawberry jam over it, leaving a small border.

Cut the dough into 12 strips and roll each strip tightly. Place rolls in a greased 9x13 inch baking pan.

Cover with plastic wrap or a towel and let rise for 30-45 minutes until puffy.

Preheat the oven to 350°F (175°C). Bake for 25-30 minutes until golden brown.

Prepare the lemon icing by beating 4 ounces of softened cream cheese, 1/4 cup of softened butter, and 2 cups of powdered sugar until smooth. Add lemon zest and milk to achieve desired consistency.

Allow the rolls to cool for 10 minutes, then drizzle or spread lemon icing over warm rolls.