Preheat your oven to 350F (175C) and lightly butter a 9x13 baking dish. Set aside.
In a large bowl, stir together sugar, brown sugar, cornstarch, cinnamon, and salt. Add peaches and drizzle with lemon juice. Toss all ingredients together until all peach slices are coated with the sugar/flour mixture. Set aside while you prepare your peach cobbler topping.
Peach Cobbler Topping
Combine flour, sugar, baking powder, and salt in the basin of a food processor¹ and pulse until combined.
Scatter (cold) butter pieces over the top of the flour mixture and pulse again until mixture resembles coarse crumbs.
Add heavy cream and milk and pulse briefly until mixture clumps together and forms a soft dough.
Stir your peaches once more and then pour peach slices (and any juices) to prepared 9x13 baking dish. Spread peaches so they’re evenly distributed in the pan.
Use your hands or a pair of spoons to evenly drop the cobbler batter over the top of the peaches. It most likely won't completely cover the peaches and that's fine (see picture in post), but try to arrange the batter so that it is distributed fairly evenly and clumps are approximately equal in size and depth so they cook evenly.
Transfer peach cobbler to 350F (175C) oven and bake for 45-55 minutes or until the topping is beginning to turn light golden brown and is cooked through (a toothpick inserted in the center of the thickest part of cobbler topping should come out without any wet batter).
Allow peach cobbler to cool for several minutes and then serve! Top with vanilla ice cream or whipped cream, if desired!
¹If you don’t have a food processor, you can combine the dry ingredients in a large bowl and stir with a spoon, then use a pastry cutter to cut the butter into the mixture until it resembles coarse crumbs.