In a medium saucepan, combine the 3/4 cup sugar, the cornstarch, and cinnamon; stir in water. Cook and stir until thickened and bubbly. Add peaches; return to boiling. Reduce heat and cook for 2 minutes more. Keep warm over very low heat.
In a medium bowl, combine flour and the 1 teaspoon sugar. Cut in shortening until mixture resembles coarse crumbs. Add buttermilk and stir until just moistened. Turn out onto a lightly floured surface. Knead dough gently for 10 to 12 strokes. Roll into a 9x6-inch rectangle.
Combine butter and brown sugar. Spread over dough to within 1/2 inch of the edge. Sprinkle pecans evenly over all. Roll up dough jelly-roll style, starting with a short side. Cut crosswise into six 1-inch pieces.
Pour hot peach mixture into an 8x8x2-inch (2-quart square) baking dish. Place pecan rolls on top. Bake in a 400 degree F oven for about 25 minutes or until golden brown. Cool for about 30 minutes and serve warm, with a scoop of ice cream, if you like. Makes 6 servings.