Preheat the oven to 350 degrees F.
While the oven is heating up, slice the peaches. I left the peels on, but feel free to peel them if you prefer. Add the brown sugar, cardamom, and ginger to a large bowl. Mix together and then add the peach slices. Gently toss together until the peaches are covered with the sugar mixture.
Put the melted butter in a 9x13 pan and swirl around, coating the bottom of the pan. Add the peach mixture to the pan. Set aside.
Then prepare the filling: place the flour, brown sugar, baking powder, cardamom, and salt in a large bowl and mix together with a fork. Then add the vanilla and melted butter and mix until a thick dough forms.
Place scoops of the mixture on top of the peaches. Spread out with a spoon - it’s ok if it’s messy and not exactly even!
Bake for 30 minutes. Then remove from the oven and sprinkle the top with turbinado sugar. Bake for another 10-15 minutes until golden brown. Finish with 2-3 minutes under a broiler to get a crunchy top.
Remove from the oven and then let stand for 15 to 30 minutes before serving. Serve with ice cream or whipped cream.