Preheat oven to 350°F (175°C) and line baking sheets with silicone mats or parchment paper.
In a saucepan over medium heat, melt the butter completely.
Add both granulated and brown sugars to the melted butter and stir until well combined and the mixture begins to simmer.
Remove the pan from heat and stir in the finely chopped almonds, flour, and salt.
Incorporate the vanilla extract and heavy cream until the batter is smooth.
Drop level teaspoons of the batter onto the prepared baking sheets, spacing them at least 3 inches apart to accommodate significant spreading.
Bake for 7 to 9 minutes until the cookies are golden brown and have formed a lace-like structure.
Allow the cookies to cool on the baking sheet for at least 5 minutes until firm before transferring to a wire rack.