Beat butter and sugar in a large mixer bowl at medium speed until combined; add vanilla bean paste and salt and beat until incorporated. Scrape down bowl as needed. Reduce speed to low and mix in flour just until incorporated and dough begins to come together in large pieces. Scrape dough out onto a piece of plastic wrap, shape into a disk and wrap well. Chill dough in the refrigerator until firm, about 30 minutes.
Preheat oven to 350°F and line two baking sheets with parchment paper.
Roll out dough to slightly less than ¼-inch thick on a lightly floured board. Use a floured 3-inch heart cutter to cut out hearts. Gather scraps to re-roll, punching out more hearts. Place hearts on baking sheets, sprinkle with sugar, and chill for 20 minutes in the refrigerator.
Bake for 14 to 15 minutes, rotating pans halfway through, until lightly golden and edges are set. Cool for 5 minutes on baking sheets, then transfer to a wire rack to cool completely.
For the topping, place chocolate chips in a microwave safe bowl and heat chocolate in 30 second intervals, stirring after each interval until melted and smooth (about 1 ½ minutes). Transfer melted chocolate to a small piping bag and drizzle over cookies. Sprinkle cookies with toffee bits and let chocolate set before serving.
