Step 1 Prepare the pastry and fit it into a 9-inch tart pan with a removable bottom. Refrigerate until well chilled, about 20 minutes. Prick the shell with a fork and bake until lightly golden, about 10 minutes. Remove from the oven and let come to room temperature.
Step 2 Heat the oven to 375 degrees and place a baking sheet on a low rack.
Step 3In a food processor, grind the almonds. Add 2/3 cup sugar, the eggs, vanilla, orange zest, Sherry and salt, and process to make a smooth, sticky paste. With the motor running, drop in the butter through the feed hole, piece by piece, and process until smooth.
Step 4Peel the pears, cut them in half lengthwise and with a spoon remove the vein for the stem and the seed pit. As you finish each pear half, slip it into a work bowl filled with a mixture of 1 tablespoon apple cider vinegar and enough water to cover all of the pears.
Step 5Spread the almond mixture in the base of the tart, using the back of a spoon to spread it as evenly as possible.
Step 6Pat each pear half dry and carefully cut it into thin crosswise slices, about 1/8 inch, keeping the pear in its original form. As you finish each pear half, lift it, using the flat of the knife as a spatula, and carefully place it in the tart pan, with the narrow stem end toward the center. Gently press down into the frangipane. Place each subsequent pear half next to the previous one in a spoke pattern until the tart is filled. Brush the pears with the melted butter and sprinkle with about 1 tablespoon sugar.
Step 7Place the tart pan on the baking sheet and bake until the almond mixture is puffed and golden and the pears are tender, 40 to 45 minutes. Serve at room temperature.