Preheat the oven to 350°F. Line a large cookie sheet with parchment paper and set aside.
Cream the butter and sugar. In a large bowl of a stand mixer fitted with the paddle attachment or a hand mixer, beat the butter and sugar together on medium-high speed for 2 minutes.
Beat the wet ingredients. Add the egg, vanilla and almond extract then beat well, until the yellow streaks are gone. Add the heavy cream and beat again until it's incorporated.
Add the dry ingredients. Whisk the flour, baking powder, baking soda, and salt in a separate medium bowl. With the mixer on low, add half of the dry ingredients, then turn the speed up to medium to incorporate it fully. Repeat the process with the second half of the dry ingredients. The cookie dough will be wet, this is what you want!
Bake the cookies. Use a heaping tablespoon or medium cookie scoop to drop the dough a few inches apart on a parchment lined baking sheet. Bake for 10 to 12 minutes or until the tops are set and no longer look wet. The cookies will spread out first then start to rise.
Cool cookies. Allow to cool on cookie sheet for a few minutes then transfer to wire rack to cool completely before frosting.
Make the frosting. Beat together the softened butter and cream cheese in a large bowl until smooth and all of the lumps are gone. Add 1 cup of the confectioner's sugar and beat on medium speed to incorporate. Add the heavy cream and vanilla extract and beat until combined and the mixture is smooth. Finish by adding the last 2 cups of confectioners' sugar and beat well until smooth.
Frost the cookies. Transfer the frosting to a piping bag and cut off the tip. Swirl the frosting onto the cooled cookies. Alternately, dollop about 1 Tablespoon of frosting on top and use the back of a spoon to spread it out.
Top with sugar and brulee. Sprinkle 1 teaspoon of granulated sugar on top of each cookie and use a torch to melt and brulee the top of the cookies. Keep the torch close to the cookie (about 1 inch away). This should take 2-3 seconds per cookie. The frosting will melt slightly—this is ok. Allow the frosting to set again before serving.