Combine sweetened condensed milk, evaporated milk, whole milk, peanut butter, sugar, and vanilla extract in an ice cream maker. Stir until sugar dissolves. Freeze according to manufacturer’s directions until it reaches soft-serve consistency.
Transfer ice cream to a one- or two-quart lidded plastic container; cover surface with plastic wrap and seal. For best results, ice cream should ripen in the freezer for at least 2 hours or overnight.