Spoon the prepared peaches into an 8-cup (2L) baking dish. Bring the brown sugar, maple syrup, lemon juice and cinnamon up to a simmer in a small saucepot. Simmer over medium-high heat for 3 minutes while stirring. Pour the sugar mixture over the peaches and stir to coat.
Preheat oven to 375°F (190°C). Combine the flour, oats, sugar, baking powder and salt in a large bowl. Using the coarse side of a cheese grater, grate the cold butter into the flour and stir it to coat. Stir the milk, egg and vanilla and add to the flour mixture, stirring until it comes together (the mixture will be soft). Spoon the dough onto fruit, leaving a little space between spoonfuls to allow for expansion as the cobbler bakes. Bake for about 50 minutes, until the cobbler bubbles around the edges, and the topping is cooked through (you can lift a piece up to check). Allow the cobbler to cool for 30 minutes before serving.