Preheat oven to 350°F (175°C). Lightly grease a 9x13 inch baking dish with butter or nonstick spray.
If using fresh peaches, peel and slice into ½-inch wedges. If using frozen, thaw completely, drain, and blot dry. If using canned, drain well and pat dry.
In a medium saucepan over medium heat, combine peaches, sugar, cinnamon, nutmeg, lemon juice, and salt. Cook for 5-7 minutes until the peaches release their juices and bubble around the edges.
In a small bowl, stir cornstarch with 2 tablespoons of cold water until smooth. Pour into the peach mixture and cook for 1-2 more minutes, stirring constantly, until thickened.
Remove from heat and stir in butter and vanilla until melted. Pour the thickened peach filling into the prepared baking dish and spread evenly.
Open both cans of cinnamon rolls and set the icing packets aside. Cut each cinnamon roll into 4 to 6 pieces and place them in a bowl, separating them gently.
Scatter the cut cinnamon roll pieces evenly over the peach filling, leaving small gaps. Sprinkle with pecans if using. Gently press the dough pieces into the filling.
Cover the baking dish loosely with foil and bake for 20 minutes. Remove foil and bake for another 15-20 minutes, until the cinnamon rolls are golden and cooked through.
Remove from the oven and let rest for 5-10 minutes. Warm the reserved icing packets if desired and drizzle evenly over the warm cobbler. Serve.