Gently warm the milk in a small saucepan until it's just bubbling, then remove from heat. Stir in the melted butter until fully combined, and let it cool until it's comfortably lukewarm to the touch.
In a large mixing bowl, combine 2 ¼ cups of the flour, yeast, sugar, salt, and lemon zest. Whisk these dry ingredients together.
Add the egg and the lukewarm milk-butter mixture to the bowl. Stir everything well with a wooden spoon. Gradually mix in the remaining 1 cup of flour, ½ cup at a time, stirring thoroughly after each addition until a shaggy dough forms.
Lightly flour a clean surface. Turn the dough out and knead it for about 5 minutes until it becomes smooth and soft. The dough should spring back slightly when you gently press it.
Cover the dough with a damp cloth or plastic wrap and let it rest on the counter for 10 minutes to relax.
On your lightly floured surface, roll the dough into a rectangle, approximately 12x9 inches. (You can use a 9x13 inch baking dish as a guide for size).
Evenly spread the strawberry compote (or jam) all over the dough, making sure to go all the way to the edges. If you're using cinnamon, sprinkle it lightly over the strawberry layer.
Using a pizza cutter or a sharp knife, slice the dough into 12 equal strips. Carefully roll up each strip, starting from one of the long sides, and place them snugly into a baking pan (a 9x13 inch pan works great).
Cover the pan and let the rolls rise in a warm spot until they've doubled in size, which usually takes about 45 minutes. Preheat your oven to 350°F (175°C) during the last part of the rising time.
Bake the rolls in the preheated oven for 23-25 minutes, or until they are beautifully golden brown.
While the rolls are baking, prepare your frosting: In a small bowl, use an electric mixer to whip together the softened cream cheese and butter until smooth and creamy.
Gradually add the strawberry compote (or jam) and powdered sugar, ½ cup at a time, beating until the frosting is creamy and spreadable. If it's too thick, add a tablespoon or two of heavy cream or milk until it reaches your desired consistency.
Once the rolls are baked, let them cool for about 10 minutes. Then, generously slather them with the delicious strawberry cream cheese frosting. For an extra touch, you can add some fresh strawberry slices on top if desired.
Serve these delightful rolls warm or at room temperature, and enjoy!