In a small bowl, combine the granulated sugar and light brown sugar.
Heat a medium stainless steel sauté pan over low-medium heat. Add the entire sugar mixture to the pan at once.
Stir gently with a wooden spoon, or heat-resistant silicone spatula, as the sugar begins to melt. The sugar will clump at first. Continue stirring gently until all of the sugar has melted and turns a smooth, rich amber color.
Remove the pan from the heat. Slowly pour in the warmed heavy cream while stirring continuously. The caramel will bubble aggressively and may firm up a little. If needed, return the pan to low-medium heat and continue stirring until smooth.
Remove from the heat and stir in the cubed butter until completely melted and incorporated.
Return the pan to low heat for 1–2 minutes, stirring occasionally, until the caramel is completely smooth and silky.
Remove from the heat and stir in the vanilla bean paste and flaky sea salt.
Allow the caramel to cool completely, then transfer to an airtight container. Store in the refrigerator for up to 3 weeks.