Learn Russian: Я боюсь недоварить рис к обеду. - I am afraid of undercooking the rice for lunch.

The prefix недо- indicates that an action was done insufficiently or fell short of the norm. Attached to the base verb варить (to boil/cook), it creates the perfective verb недоварить, meaning "to undercook." The opposite prefix for excess is пере-, making "to overcook" переварить.

Could I write this as two words, не доварить, and would it mean the same thing?

No, they have different nuances. As a single prefix, недо- means the action was technically completed, but the result was insufficient (the rice is cooked, but it is too hard). If written as two words (не доварить), it is the negative particle не plus the verb доварить (to finish cooking), which means the cooking process was simply stopped before it was finished.

Why is рис in the accusative case here? Doesn't бояться (to be afraid) require the genitive case?

You only use the genitive case after бояться when you are afraid of a noun (e.g., Я боюсь темноты - I am afraid of the dark). Here, you are afraid of an action, so боюсь is followed by the infinitive verb недоварить. The word рис is the direct object of недоварить, so it takes the regular accusative case. Because рис is masculine and inanimate, its accusative form looks exactly like its nominative form.