Make the biscuits:
Position a rack in the center of the oven and heat the oven to 400°F. Line a baking sheet with parchment or a nonstick liner.
Put the flour, brown sugar, baking powder, salt, and nutmeg in a food processor fitted with a steel blade. Pulse briefly to blend.
Cut the butter into small pieces and add to the food processor. Pulse until the butter is cut into pieces the size of large breadcrumbs, 6 to 8 pulses.
With the food processor running, immediately pour 1 cup of the cream through the feed tube and process just until the ingredients are moistened.
Turn the mixture out onto a lightly floured work surface and knead a few times just until smooth. Pat the dough into a 3/4-inch-thick circle or rectangle. Dip a 2-3/4-inch round plain-edge biscuit cutter in flour and then cut straight down through the dough to form the biscuits. (Dip the cutter in flour before cutting each biscuit and don't twist the cutter, because it will seal the edges and keep the shortcakes from rising as they bake.)
Transfer the shortcakes to the lined baking sheet, leaving at least an inch between them. Gather the scraps together, knead briefly to smooth the dough, and shape into a 3/4-inch-thick circle or rectangle. Cut out more shortcakes. Repeat as often as necessary to use most of the dough (there will be a little left over).
With a pastry brush, lightly coat the tops of the biscuits with the remaining 1 tsp. cream and then lightly sprinkle them with demerara sugar.
Bake until the bottoms are slightly golden, 14 to 16 minutes. Remove the baking sheet from the oven and let the biscuits cool completely on a rack before serving. While the biscuits cool, marinate the peaches and make the honey whipped cream.
Assemble the shortcakes:
Using a serrated knife, slice each biscuit in half horizontally. Set the bottom half on an individual serving plate and spoon about one-eighth of the marinated peaches, a scant 1/4 cup, over the biscuit. Cover the peaches with a generous spoonful of the honey whipped cream. Put the top of the biscuit on the cream. Drop a small dollop of whipped cream on the biscuit top, if you wish. Repeat with the remaining biscuits. If you have any peach slices left, arrange them around the plates. Serve immediately.