Position a rack in the center of the oven and preheat to 400 degrees. Meanwhile, in a large bowl, combine the peaches, 1/4 cup sugar and 2 tbsp. flour; toss well.
In another large bowl, whisk together the remaining 1 1/2 cups flour, the cornmeal, 1/3 cup sugar, the lemon zest, baking powder, baking soda and salt.
Set aside 1 tbsp. butter to soften at room temperature. Rinse your hands with cold water and dry them (this is to keep them cool when you grate the butter). Grate the rest of the stick of butter on the large holes of a box grater; toss with the flour mixture. Refrigerate.
Use the reserved 1 tbsp. butter to grease a shallow 9-by-13-inch baking dish. Transfer the peach mixture to the dish, cover snugly with foil and bake for 20 minutes.
About 5 minutes before the baking time is up, drizzle 1 1/4 cups heavy cream into the flour-butter mixture and stir lightly with a fork until just combined.
Uncover the peaches and distribute the biscuit mixture on top in clumps, covering as evenly as you can. Bake until the top is nicely golden and the peaches are bubbling, 20 to 25 minutes. Let cool for at least 30 minutes before serving.
While the cobbler cools, whip the remaining 1 1/4 cups cream and 4 tsp. sugar until barely stiff; refrigerate until ready to serve. Spoon the slightly warm cobbler onto plates and dollop the whipped cream on top.