1. Preheat the oven to 350 degrees F. 
2. To make the cookies: Combine butter, sugars, lemon zest, and vanilla in the bowl of a stand mixer with the paddle attachment. Mix on medium speed until all ingredients come together and are light and fluffy. Add the egg. Sift together the flour, baking soda, nutmeg, and salt, and add to the butter mixture in three parts, waiting until each is well mixed before adding the next. Add the oats last, mixing just until combined. Chill the dough in the freezer for 5 minutes. 
3. Transfer the dough to a large surface covered with a layer of parchment paper. Top with another layer of parchment and gently roll the dough into a 1/4-inch-thick sheet. To prevent the cookies from sticking as you cut them, carefully remove the top layer of parchment and drizzle some flour over the sheet of dough. Replace the parchment, flip the dough, and release the parchment on the other side. Cut the dough into 2 1/2-inch round cookies and space about 1/2 inch apart on an ungreased cookie sheet. Gather any leftover scraps of dough and roll and cut as described above. Repeat until you have no dough left. Bake the cookies for 15 to 20 minutes, turning the pan 90 degrees halfway through baking, until golden brown in color but still soft in the center. Transfer the cookies to a cooling rack. Let cool completely before filling.

For the filling:

1. To make the filling: Bring the water and 3 tablespoons of the sugar to a boil in a small heavy-bottom saucepan. Once a dark brown color is achieved and the sugar looks like caramel, remove from the heat and very carefully whisk in the cream. Allow to cool. In the mixer with the paddle attachment, combine the butter with the remaining 4 tablespoons sugar and mix until the sugar is completely dissolved. Add the salt and vanilla, and once they are incorporated, turn the mixer down to a low speed and add the cream cheese and the caramel. Mix until fully incorporated Place half of the cookies with the top side (the most attractive) down. Using a piping bag or a spoon, evenly distribute the filling among the cookies, and close into sandwiches with the remaining cookies. Gently press down. Serve immediately or store the cookies in a cool place.