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Place rack in center of oven and preheat to 375 degrees F. Lightly coat a 9x9-inch casserole dish with nonstick spray.
To quickly and easily peel the peaches: Bring a very large pot with enough water to cover the peaches to a boil. While the water comes to a boil, prepare an ice bath by placing several generous handfuls of ice cubes in a large bowl and then filling it with cold water. With a small, sharp knife, score the bottom of the peaches with an "X." Once the water is boiling, with a slotted spoon or tongs to protect your fingers, gently lower half of the peaches into the water. (You want to add the peaches in two batches so that the water temperature does not rapidly drop.) Boil for 1 minute. With the spoon, remove peaches from the water and plunge into the ice bath to stop the cooking. The skins can now be easily slipped off with your fingers. Repeat with remaining peaches. (Every now and then, you'll get a stubborn peach that still won't peel and have to use a knife, in which case, my apologies and you deserve an extra serving of the finished peach crisp!)
Cut the peeled peaches into thick, 3/4-inch wedges (about 8 per peach, depending on the size). Place the wedges in a medium bowl and stir in the honey, flour, lemon zest, vanilla extract, and nutmeg. Set aside while you make the topping.
Prepare the topping: In a medium saucepan, heat the butter and oil over medium heat, until the butter melts. Whisk in the brown sugar and granulated sugar until blended (The oil and butter will still be a little separate from the sugar, but the sugar should not have any lumps). Once combined, sprinkle in the oats, white whole wheat flour, cinnamon, and salt. Switch to a rubber spatula and fold to combine, stirring until the ingredients are evenly moistened. The mixture will be a little crumbly. Last, stir in the almonds.
Give the peach filling mixture a few additional stirs, then transfer it to the prepared baking dish, along with any juices that have collected in the bowl. Sprinkle the topping evenly over the fruit.
Place the crisp in the oven and bake for 20 minutes, then remove it from the oven and lightly cover it with aluminum foil to protect it from over browning. Return to the oven and bake for an additional 10-15 minutes or until the topping is lightly golden and the filling is hot and bubbly.