"Hearty laugh" refers to a loud and genuine laughter that comes from deep within someone and shows their genuine enjoyment or amusement. Full definition
She has a big personality as do I, and I think we would have good easy conversation and big hearty laughs. (theeverygirl.com)
«I'm happy that my children are not farmers,» he says with a long hearty laugh. (earthjournalism.net)
Its sly humor is perhaps the ace up the sleeve — Buschel knows how to disarm a tense situation with the right combination of humorously dark blows, and he lands each and every one with hearty laughs. (indiewire.com)