If using fresh or drained canned pineapple, arrange in a single layer on a rimmed baking sheet lined with parchment paper, or in a ziplock bag, and freeze until firm, about 1 hour.
Combine frozen pineapple, coconut milk, rums, sugar, lime juice, and vanilla bean paste in a blender; process until smooth and creamy, about 2 minutes. Place blender pitcher in refrigerator, and let piña colada mixture rest until flavors meld, about 30 minutes. Return pitcher to blender base; add ice cubes, and process until thick and smooth, about 30 seconds. Divide among tulip wine glasses or hurricane glasses. Float additional dark rum on top of each drink to taste, and garnish as desired.