Combine 2 1/2 cups sugar, water, cinnamon syrup, and cinnamon sticks in a large saucepan over medium heat. Add pears, cover, and cook for 20 minutes. Strain pears and save poaching liquid for future recipes if desired. Let pears cool.

Cut pears lengthwise into mini slices, leaving the stem end intact.

Preheat the oven to 350 degrees F (175 degrees C). Grease 4 mini oven-proof skillets.

Roll out pie pastry and cut out circles 1/2- to 3/4-inch larger than the mini skillets. Fit dough into the skillets, leaving room for overhang. Lay foil or parchment paper on top of the dough and place pie weights or beans on top.

Bake pie crusts in the preheated oven for 10 to 15 minutes to reduce any shrinking of the crust. Remove foil and weights and let crust cool while preparing the filling; leave oven turned on.

Whisk together 2 cups sugar, flour, nutmeg, and salt in a small bowl and set aside.

Whisk eggs in a large bowl to break them up. Mix in buttermilk, lemon juice, and lemon zest until well combined. Add the sugar-flour mixture and mix well. Stir in melted butter and vanilla paste until just combined.

Divide walnuts among the prebaked crusts. Add pears. Pour about 1 cup of the buttermilk mixture into each skillet. Place skillets on a large baking sheet.

Bake for 35 minutes. Reduce heat to 340 degrees F (170 degrees C) and bake until center is set but still slightly jiggly, about 15 minutes more. Place pies on a wire rack and let cool completely.