6 ounces soft fresh goat cheese (about 3/4 cup packed)
1 tablespoon fresh lemon juice
1/4 teaspoon coarse kosher salt
3 medium Gala apples, peeled, quartered, cored, cut into 1/8-inch-thick slices
3 tablespoons unsalted butter, melted
3/4 cup honey (preferably dark), divided
1/2 teaspoon (scant) ground allspice
1. Line 2 rimmed baking sheets with parchment paper.
2. Roll out each puff pastry sheet on lightly floured surface to 11-inch square. Using 5-inch-diameter cookie cutter or bowl, cut out 4 rounds from each pastry sheet, forming 16 rounds total. Divide 8 pastry rounds between prepared baking sheets; pierce rounds all over with fork. Using 3 1/2-inch-diameter cookie cutter or bowl, cut out smaller rounds from center of remaining 8 rounds (reserve 3 1/2-inch rounds for another use), forming eight 5-inch-diameter rings.
3. Brush outer 1-inch edges of 5-inch rounds on baking sheets with beaten egg; top each with 1 pastry ring. Freeze at least 30 minutes. These can be made 1 day ahead. Cover and keep frozen. Do not thaw before continuing.
4. Preheat oven to 375°F. Mix cheese, lemon juice and salt in bowl; spread mixture inside rings on frozen pastry rounds. Overlap apple slices atop cheese. Mix butter and 1/4 cup honey in small bowl; brush over apples. Sprinkle with allspice. Bake until apples are tender and pastry is golden, about 35 minutes.
5. Place tartlets on plates. Drizzle 1 tablespoon honey over each and serve warm or at room temperature.
6. Bake the tartlets four to six hours ahead, then store them uncovered at room temperature. Rewarm in a 350°F oven for 5 to 10 minutes. Drizzle tartlets with honey just before serving.