Heat oven to 350 F.
Combine peaches and blackberries in an 8- or 9-inch skillet or a 1-quart ovenproof casserole.
Combine cornstarch, brown sugar and water in a small saucepan. Cook over low heat until thick, stirring constantly. Add lemon juice; pour over fruit.
To make the cobbler crust: In a small bowl, combine flour, sugar, baking powder and salt. Beat in milk and butter until smooth.
Spread cobbler crust mixture over fruit.
Combine sugar and nutmeg; sprinkle over crust.
Bake until bubbly and browned, 30-40 minutes. Garnish with Crème Fraîche or sweetened whipped cream, if desired.
Combine cream and sour cream in a glass bowl; cover with plastic wrap.
Let stand at room temperature until thickened, about 8 hours in warm weather, up to 24 hours in cold weather.
Refrigerated, covered, 4-6 hours before using.
Tip: The flavor of Crème Fraîche becomes more tart the longer it is refrigerated. It will keep up to 2 weeks in the refrigerator.