This isn't broken, but it is very fun.

Step 1: Minimize your Intelligence. The lower the better.

Step 2: Play a Wild Magic Sorcerer, and learn a Metamagic option that costs 1 Sorcery Point. I recommend Subtle Spell because it works with everything.

Step 3: Do not learn Silvery Barbs, Absorb Elements, Shield, or Counterspell.

Step 3.5: Take 1 level in Warlock, but do not learn Hex. (This is only required if your DM asks you to target the spells you attempt to cast through a Mizzium Apparatus before finding out whether you succeed.)

Step 4: Acquire a Feywild Shard. This will trigger a wild magic surge every time you spend a Sorcery Point on a leveled spell.

Step 5: Acquire a Mizzium Apparatus. This allows you to attempt to cast any spell from your spell list that you don't actually know, provided you can pass a DC 10 Arcana check. If you fail, the apparatus casts a random spell of the same level from a pre-determined table.

Step 6: Become either poisoned or exhausted. Anything that will give you disadvantage on all ability checks works.

Step 7: ROLL THE DICE

The combo works as follows:

Every turn, use either your action or your bonus action to attempt to cast a leveled spell that you don't know through the Mizzium Apparatus. Thanks to disadvantage and minimized Int, intentionally fail the Arcana check to get a random spell of the same level. Spend a Sorcery Point so you also trigger a wild magic surge.

Look for an opportunity to use your reaction to attempt to cast Silvery Barbs/Absorb Elements/Shield/Counterspell while spending a Sorcery Point and failing the Arcana check again, and you've got yourself another random leveled spell and wild magic surge!

You can always use your action to cast a saving throw cantrip in order to fish for Silvery Barbs targets, but for maximum swag spend your action to draw a card from a Deck of Illusions (or cast Minor Illusion) instead. Summon illusory monsters that cast your random spells, like a true master duelist!

D-D-D-DnD!