The puzzle is to gain "infinitely-many" cards in one turn: more precisely, use a finite, fixed-size deck to gain a number of cards in one turn that is limited by the supply only. So if the supply limits were increased by 10x, then the same deck could gain around 10x as many cards in one turn.
This is pretty easy using King's Court, so there are really two puzzles: do it with King's Court and without.
A King's Court solution:
Have 4 Highways or Bridges in play, have your entire deck in your hand, and have King's Court, Ironworks, and Smithy in hand.
KC-Ironworks to gain KC, Ironworks, Smithy. Then play the Smithy to draw the three cards you just gained. Repeat until supplies run out. Each iteration actually also nets you +1 action.
A solution without King's Court:
Have 2 Highways or Bridges in play. Have your entire deck in your hand. Your hand must contain Black Market, 2 Border Villages, Crossroads, 3 Horns of Plenty, and 8 green cards.
Play BV twice, play BM and use it play the horns to gain: Black Market, Border Village+Crossroads, Border Village+Mandarin. (This is possible because BV costs 4 after the Highway effect, and you have BV, BM, Horn, and Highway in play.) The on-gain effect of the Mandarin causes the horns to go on top of your deck. Now, play Crossroads to draw 8 cards from your deck: three horns, a Black Market, two BVs, a Crossroads, and a Mandarin. Repeat until supplies run out.