Heat oven to 375. In a medium bowl, gently toss the peach slices with the lemon juice and vanilla. Mix the dry filling ingredients in a small bowl, then fold into the peaches. Divide the filling between two 12 ounce greased ramekins, then bake for 10 minutes on the middle rack of your oven.
While the filling bakes, mix the dry topping ingredients together in a medium bowl. Cut the butter into small pieces, then quickly incorporate the butter into the flour mixture with a fork. Incorporate 1 tablespoon of the cold milk, followed by the remaining tablespoon. The mixture might seem dry at first, but it should come together once you work it into a ball. If it's still dry, add a little more milk until it can come together. Divide the dough into two, then flatten both into disks to cover the peach filling. Freeze the dough disks until your peaches are out of the oven. Once the peaches have cooked for 10 minutes, place the dough on top of each dish, then lightly brush with milk and sprinkle with sugar. Place the ramekins on a baking sheet, then bake for 30 minutes, or until the filling is hot and bubbly, and the crust is lightly golden brown. Let the cobbler rest for 20 minutes before enjoying. Top with yogurt or ice cream, with a couple peach slices to garnish.