Begin by creaming together 1 cup of softened butter and 3/4 cup granulated sugar in a large mixing bowl until light and fluffy, about 3-5 minutes. Beat in 2 large eggs and 2 teaspoons of vanilla extract. Gradually mix in 2 1/4 cups of all-purpose flour until just combined, ensuring not to overmix. The dough should be soft and slightly sticky.

Using a cookie scoop or tablespoon, drop rounded balls of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart. Refrigerate the dough balls for 30 minutes, allowing them to firm up slightly.

Preheat your oven to 350°F (175°C). Once the dough has chilled, bake the cookies for 12-15 minutes, or until the edges are golden and the centers are set but still soft.

In a medium saucepan over low heat, combine 1 cup of heavy cream, 1/4 cup granulated sugar, and 4 egg yolks. Whisk continuously until the mixture thickens and coats the back of a spoon, about 5-7 minutes. Remove from heat, stir in 1 teaspoon of vanilla extract, and let it cool.

Once your cookies have completely cooled, use a piping bag or a spoon to fill the centers of half the cookies with the chilled pastry cream. Press the remaining cookies on top to create sandwiches.

Sprinkle a thin, even layer of granulated sugar (about 1 tablespoon per cookie) over the filled cookies. Using a kitchen torch, caramelize the sugar until it melts and forms a golden-brown crust.

Allow the assembled Creme Brûlée Cookies to sit for a few minutes after caramelizing to let the sugar topping harden slightly. Serve them warm.