Whisk the sifted powdered sugar and fine sea salt together in a large bowl to distribute the salt evenly and break up any remaining sugar clumps.
In the bowl of a stand mixer fitted with the whisk attachment, beat the peanut butter and maple syrup on medium speed for 30–45 seconds until glossy and completely smooth.
Add the cool room-temperature butter in 3 additions, beating after each until incorporated. Once all the butter is in, increase to medium-high and whip for 2–3 minutes until lighter in color and satiny.
Reduce to low and add about half of the sugar mixture. Mix just until most of the sugar disappears, then let the bowl sit for 1 minute to allow the sugar to hydrate—this helps the frosting smooth out faster.
Add the vanilla bean paste and 2 tablespoons of the heavy cream. Beat on medium for 1 minute, scraping the bowl and beater as needed to capture any pockets of peanut butter.
With the mixer on low, gradually add the remaining sugar. Drizzle in the last tablespoon of cream (plus a splash more if you prefer a softer spread) until the frosting reaches a medium-firm consistency. Increase to medium-high and whip for 60–90 seconds to aerate.
For an extra-smooth finish, switch to the paddle attachment and mix on low for 20–30 seconds to gently deflate large air bubbles. If too thick, blend in additional cream 1 teaspoon at a time; if too soft, add powdered sugar 1–2 tablespoons at a time.
Use right away or chill for 10 minutes to slightly firm before piping. Stir briefly before frosting cakes or cupcakes.