Preheat oven to 375ºF
In a small pot over medium heat, stir together the sugar and enough water to make it look like wet sand. Simmer until it turns to a deep golden brown. Remove from heat and pour equal amounts into the bottom of each cup of a 6-cup muffin tin. Top with about 4 slices of pear, making sure they fit snug. Top with a drop of vanilla extract and a squeeze of lemon juice. Repeat until each muffin cup is filled.
Place the puff pastry on your work surface and cut 6 rounds with a cookie cutter or cup that is the size of each muffin tin cup. Place a pastry round on top of each pear-filled cup, brush with the beaten egg and bake until golden brown and cooked through, about 15-20 minutes.