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Preheat oven to 400F for crusts.
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(Temperature will be reduced to 350F for the filling.
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).
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Coat 12 (1/2-cup) muffin cups with cooking spray.
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To prepare crust:
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Combine pecans, granulated sugar and salt in a food processor; pulse until the nuts are finely ground.
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Add 1 3/4 cups flour; pulse to combine.
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With the motor running, add butter a few pieces at a time until well incorporated.
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Then add egg and water and process until starting to clump together.
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Using about 1/4 cup each, press the dough into the bottom and all the way up the sides of each muffin cup to form a crust.
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Prick the bottom with a fork.
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Bake until the crusts are set and the edges are just beginning to brown, 6 to 8 minutes.
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Let cool on a wire rack.
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Reduce oven temperature to 350F.
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To prepare filling:
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Combine apples, 1/3 cup brown sugar, lemon juice, 1 teaspoon cinnamon and nutmeg in a large saucepan.
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Place over medium-high heat and cook, stirring frequently, until the sugar melts, about 1 minute.
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Reduce the heat to medium, cover and cook, stirring occasionally, just until the apples start to soften, 6 to 8 minutes.
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Remove from the heat and stir in 1 tablespoon flour.
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Divide the filling among the crusts (about 2 tablespoons each).
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To prepare topping:
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Combine oats, 2 tablespoons each flour, brown sugar and oil, 1/4 teaspoon cinnamon and pinch of salt in a medium bowl.
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Press the topping onto each mini pie (about 1 tablespoon each).
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Bake until the topping is beginning to brown, 20 to 25 minutes.
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Remove from the oven and nestle a cheese wedge in the center of each pie.
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Return to the oven and bake until the cheese is melted, about 5 minutes more.
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Let cool at least 15 minutes before serving.
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Run a sharp knife around the edge of each mini pie to loosen it, then gently pry from the muffin tin with a butter knife.
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Serve warm.
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Make Ahead Tip: Prepare crust and topping (cover and refrigerate separately for up to 3 days).
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Equipment: Muffin tin with 12 (1/2-cup) cups.
