Lightly flour your surface and roll out crescent roll (or 1 sheet thawed puff pastry) until about 1/4 inch thick (leave the other sheet in the refrigerator).
Brush puff pastry with melted butter, leaving 1 inch of space around the edges.
Evenly add strawberry jam then layer with strawberry slices and sprinkle on ground cinnamon over buttered area.
Tightly but gently roll the dough up. Use a little melted butter on the open edge of the roll to seal the seam.
Using a sharp knife, slice the roll into six pieces.
Place each roll inside a parchment paper lined baking dish. Place the dish in the refrigerator as you repeat the above steps with the last sheet of puff pastry if using.
Bake the cinnamon rolls in preheated oven for 25-30 minutes or until golden (watch carefully!).
While rolls are baking, make the icing by mixing all remaining ingredients together (confectioner's sugar, butter, milk and jam) until nice and smooth and pourable. If needed, add a teaspoon more of milk until it is pourable.
Drizzle over cinnamon rolls when they are fresh out of the oven and enjoy. Happy Baking!