At first I thought you would only draw one card. But I think the rules have been tweaked on this since I last did dastardly stuff like this…
109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn't include the word "card," "spell," "source," or "scheme," it means a permanent of that card type or subtype on the battlefield.
Thus the Bludgeon Brawl enchantment only refers to noncreature, non-Equipment cards already on the battlefield. It's a continuous effect. Note it does not affect cards in your hand or spells on the stack. That's why I thought maybe you'd only draw one card.
But here's the relevant rules. Emphasis is mine.
603.6b Continuous effects that modify characteristics of a permanent do so the moment the permanent is on the battlefield (and not before then). The permanent is never on the battlefield with its unmodified characteristics. Continuous effects don't apply before the permanent is on the battlefield, however (see rule 603.6e).
Example: If an effect reads "All lands are creatures" and a land card is played, the effect makes the land card into a creature the moment it enters the battlefield, so it would trigger abilities that trigger when a creature enters the battlefield. Conversely, if an effect reads "All creatures lose all abilities" and a creature card with an enters-the-battlefield triggered ability enters the battlefield, that effect will cause it to lose its abilities the moment it enters the battlefield, so the enters-the-battlefield ability won't trigger.
603.6b is confirmed and reframed by 611.3c:
611.3c Continuous effects that modify characteristics of permanents do so simultaneously with the permanent entering the battlefield. They don't wait until the permanent is on the battlefield and then change it. Because such effects apply as the permanent enters the battlefield, they are applied before determining whether the permanent will cause an ability to trigger when it enters the battlefield.
Example: A permanent with the static ability "All white creatures get +1/+1" is on the battlefield. A creature spell that would normally create a 1/1 white creature instead creates a 2/2 white creature. The creature doesn't enter the battlefield as 1/1 and then change to 2/2.
Therefore, guess what Johnny? When Ichor Wellspring enters the battlefield, due to the continuous effect of the Bludgeon Brawl, it thinks that it has always been an Equipment and triggers Puresteel Paladin's ability! You get to draw two cards!