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To make the dough: Whisk the flour and salt together in a medium bowl. Work in the butter until the mixture is crumbly.
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Whisk the egg, vinegar, and 2 tablespoons water together in a small bowl. Drizzle it into the flour mixture, tossing to moisten evenly.
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Fold the dough over on itself until it comes together, drizzling in more water as needed to moisten any dry patches.
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Pat the dough into a slab about 1/2" thick, wrap, and refrigerate for at least 1 hour.
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To make the filling: Use a mixer to beat the eggs, brown sugar, and salt until smooth. Add the maple syrup, vinegar, melted butter, and vanilla and beat until thoroughly combined.
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Preheat the oven to 375°F. Have on hand a lightly greased or non-stick 12-cup standard muffin pan.
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To assemble the tarts: Roll the dough 1/8" thick. Cut 4" circles and press them gently into the muffin tins. Fill each tart two-thirds full with the filling.
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Bake the tarts for 20 to 25 minutes, until the crust is golden and the filling is bubbly. Remove from the oven and cool completely before unmolding.
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Wrap and store in the refrigerator for up to 1 week; or freeze for longer storage, up to 2 months.
