In a stand mixer, with paddle attachment, beat butter until light and fluffy, about 4-5 minutes. On the lowest speed, beat in the mascarpone cheese with butter until well combined. Go slowly or you risk the cheese breaking. Once combined, slowly beat in cool (but still liquid) caramelized white chocolate. Add powdered sugar, a generous tablespoon at a time, beating slowly to combine. After adding about half the powdered sugar, add in the salt and vanilla bean paste. Beat until well combined. Add the remaining half of the sugar, a generous tablespoon at a time, beating until well combined. Once all the sugar is added, beat frosting on med-high until smooth. Using a palette knife or spatula, spread frosting on top of cooled pumpkin bars.