Mix the sugars: In a small bowl, combine the granulated sugar and light brown sugar. Set aside.
Melt the sugar: Heat a medium stainless steel sauté pan over low-medium heat. Add about ¼ of the sugar and stir gently with a wooden spoon or heat-resistant silicone spatula until it starts to melt. Gradually add the remaining sugar in ¼ increments, stirring until each portion melts before adding the next. (The sugar will clump at first — keep stirring gently until it turns a smooth, rich amber color.)
Add the cream: Remove the pan from heat. Slowly pour in the warmed heavy cream, stirring continuously. If the caramel firms up, return the pan to low-medium heat and stir until smooth. Continue until all the cream is incorporated.
Add the butter: Off the heat, stir in the cubed butter until fully melted and combined.
Finish cooking: Return the pan to low heat for 1–2 minutes, stirring occasionally to fully incorporate and achieve a silky texture.
Flavor and salt: Remove from heat and stir in the flaky sea salt and vanilla bean paste.
Cool and store: Allow the caramel to cool completely. Transfer to an airtight container and store in the fridge for up to 3 weeks. Reheat gently before using, if needed.