Preheat the oven to 350F (175C) and line a baking sheet with parchment paper. You will need to bake in batches, so make sure you have enough parchment paper or several silicone mats.
In a saucepan, add the butter, white and brown sugar, honey, and heavy cream. Heat over medium heat, stirring occasionally, until the butter has melted. Wait until the mixture comes to a boil, then remove from heat.
Add the vanilla extract and salt, and mix well.
Add the flour and ground almonds, and mix thoroughly. The batter will be very runny. Transfer it into a clean bowl and allow it to rest for 10–15 minutes. This will help it cool down and become firmer, making it easier to work with.
Scoop 8 dough balls (2 teaspoons each) onto the prepared baking sheet. Make sure they have enough space to spread, as they will spread a lot during baking.
Bake for 10 minutes (rotate the baking sheet halfway through if your oven has hot spots) or until the cookies have spread, stopped bubbling, and turned golden brown.
Remove the cookies from the oven. If you want a perfect round shape, use a large round cookie cutter to pull the edges of the cookies gently back toward the center.
Slide the parchment paper from the baking sheet onto a countertop and allow the cookies to cool for 10 minutes.
Peel the cookies off the paper and place them on a cooling rack to cool completely before serving.