Soak tapioca pearls overnight in cold water or for 1–2 hours in hot water. Drain.
In a large saucepan, bring milk, cream, and sugar to a gentle simmer over medium heat, stirring occasionally (don't boil).
Add tapioca, reduce heat to low, and simmer 20–25 minutes, stirring often, until pearls are translucent and mixture thickens.
In a bowl, whisk eggs. Slowly whisk in ½ cup hot tapioca mixture, then pour back into the pot, stirring constantly.
Cook 2–5 more minutes on low, stirring, until pudding coats the back of a spoon.
Remove from heat and stir in butter, salt, and vanilla bean paste.
Pour into a shallow dish. Press plastic wrap directly onto the surface if cooling to prevent a skin.
Once cool, remove plastic wrap.
Sprinkle ⅓–½ cup sugar evenly over the top.
Broil on the top rack for 1–3 minutes until sugar melts and bubbles (watch closely).
Finish caramelizing with a kitchen torch. Let sit 1–2 minutes to set.
Toss all ingredients in a bowl to coat berries.
Let sit at room temperature for 20–30 minutes until juicy, stirring occasionally.
Chill until ready to serve. Spoon over or beside the pudding.
