that with verb after it

Words like "that", "which", and "who" don't have any intrinsic plurality, they inherit it from their antecedents:

• the box that is on the table
• the boxes that are on the table

Interestingly, the example in the question could in theory be correct either way:

• a handful of friends that want to hang out
• a handful of friends that wants to hang out

with the second case having "that" refer to "handful" rather than to "friends". That would be somewhat awkward and unusual though. It might be more common if the word "group" were used rather than "handful".

Another example would be:

• a quorum of judges that find him guilty (each judge finds)
• a quorum of judges that finds him guilty (the quorum finds)