The phrase "Throw some cheese on a broke cracker" can be deemed funny or ironic for a multitude of reasons due to its multiple layers of meaning with a play on words, idioms, cultural/jargon influences, and societal perceptions. The humor or irony can be broken down into different aspects as follows.
Firstly, the sentence can be interpreted literally. In a literal sense, the phrase seems to suggest the action of placing cheese on a broken cracker, envisioning a chaotic and messy scenario which could be humorous due to its absurdity. The image of someone actually trying to throw cheese on a broken cracker can seem ridiculous and thus funny.
Secondly, the word 'cracker' in American jargon refers to a white person, typically of lower socioeconomic status. Meanwhile, 'cheese' is sometimes used metaphorically to refer to wealth or money. From this perspective, the phrase humorously proposes a solution to poverty, i.e., just ‘throwing’ wealth on a poor person.
Thirdly, there's the visual humor in the metaphor. The idea of someone being 'broke' (financially struggling) conjures up an image of being shattered or broken like a cracker. ‘Throwing cheese’ on such a person can be imagined as a bizarre, ineffective band-aid solution, further augmenting the humor in the phrase.
The irony starts where 'cheese' is a common food item and something relatively cheap while also being a slang term for money or wealth. The phrase is therefore reversing the value of 'cheese', transforming it from something ordinary to something seemingly capable of fixing poverty, an overwhelming societal issue.
Additionally, if we take 'Throwing some cheese on' to mean lavishing money or goods on someone, it insinuates that doing so would somehow fix the person labelled as a 'broke cracker.' The irony here is derived from the generally accepted understanding that simply throwing money at a problem, especially something as complex as poverty, rarely provides a lasting solution. Hence, this statement could be seen as an ironic commentary on certain social policies or attitudes.
Lastly, throwing cheese on a literal cracker is usually done to enhance its taste, to 'fix' the blandness. This makes it ironic when applied to a 'broke cracker,' since monetary issues are far more complicated than the blandness of a cracker. The sentence simplifies a significant socio-economic issue, making it funnily reductionist, thus adding to its irony. Throw some cheese on a broke cracker