Okay, seriously though, I don't like dice in games. I have some 40-50 board games I believe, some of them have dice, and they are probably the worst part of all of them. Comparatively, I love them in role-playing games. Why? When I play board games, I want agency. When I play role playing games, I don't. I could go into depth, but basically, I want unpredictability in my stories, but not in my intellectual exercises. I like cards though, make of that what you will.
So, let's explore "upgrading dice."
Formula D is a roll-and-move racing game where on your turn, you can 'change gear', replacing your dice with a 'better' or 'worse' one, the higher gear ones having higher range and variance. The core gameplay comes down to choosing the optimal gear, as you can't move too quickly through swingy areas, or you will suffer damage.
Quarriors! is the first game that used the deckbuilding formula for dice instead of cards. Basically, you have a bag of dice that represent monsters (or spells maybe). At the start of the game, you start with some rubbish ones, but during the course of the game, you use those dice to buy better dice, slowly accumulating a strategy that ideally beats your opponent's.
Rattlebones is a roll-and-move game where you have a set of dice, and by landing on certain spaces, you can physically replace the faces of your dice according to the space. You win the game by accumulating victory points, which can happen by moving around on the lap, landing on certain spaces, or by victory point generating faces.
Savage Worlds is a Role-Playing Game where your capability in stats are represented by dice, and you can upgrade them from d4 up to d12.
When it comes to dice games, while it's not necessarily related to upgrading dice, it's worth mentioning the movement of roll-then-spend mechanics, like Kingsburg, Troyes, Castles of Burgundy and co. They have a more euro-centric use of dice, in which they operate like the pawns of worker-placement games, where the actions available to you are dependent on the faces of the dice, but faces are only contextually better than each other, and not objectively so.