Very funny but a bit complicated.
They are vegan and have gluten but no nuts
vegan = vegetarian
gluten (people who check for gluten in everything they eat) = euphemism for politically correct, leftist, attention seeking. Have gluten means he is not that type of a person.
no nuts = can be either one of (1) no balls, or (2) not crazy/stupid
So, in this joke this girl is saying that, she likes her men just like those cookies - vegan and have gluten but no nuts.
"how I like my men" = that's how I like my men = that's the kind of men I like. You just have to look at all the "how I like my men" quotes to appreciate this type of jokes. Here are two examples:
I like my men like I like my cheesecake - rich and white / rich and yellow
I like my men like I like my coffee - strong, black and able to keep me up all night.
HR Jar = a jar set up by the HR department for collecting fines. Any time an employee said something politically incorrect, they pay a fine of a loonie (a dollar) into the jar.