Preheat oven to 350 degrees and grease a 2 1/2 quart baking dish. Set aside.
In a medium sized saucepan, heat peaches, sugar, flour, water, cinnamon, and nutmeg over med-low heat, for about 5-6 minutes, stirring occasionally. Allow mixture to cool, about 5 minutes.
Pour peaches into the baking dish.
Cut each cinnamon roll into fourths, and sprinkle the dough evenly over the top of the peaches.
Tent a piece of foil over the baking dish, and bake for 20 minutes.
Remove the foil, and bake the cobbler for an additional 20-25 minutes, or until peaches are bubbling and cinnamon rolls are golden brown.
Whisk powdered sugar, vanilla extract, and 1 Tbsp heavy cream together. If the glaze is too thick, add the additional Tbsp of heavy cream.
Once the glaze is at your desired consistency, drizzle it over the top of the cinnamon roll peach cobbler.
Store leftovers in the fridge.