In most situations, they would be uncountable. You would ask "how many beans" only when you truly expect the answer to be a number of beans rather than a measurement. For instance, someone might put some beans in a jar and hold a contest to guess "how many" beans are in the jar.
Meanwhile, you could ask "how many" about countable units of measurement.
"Cook some beans."
"How many grams?"
In the comments some have suggested that "How much beans do you want" sounds odd. I think that's just because of the situation. I think "How much beans should I cook" sounds perfectly fine, because one expects a detailed answer to the vague question (100 grams, or 1.5 kg, or half a liter). Serving someone and asking "how much beans do you want" is odd simply because it's hard to answer. "Uh... this much?"