The sound of Irish laughter is music to Sharon Horgan’s ears. “Making your home country laugh or happy is actually quite addictive,” Ms. Horgan says. It is one of the reasons she decided to produce “Frank of Ireland,” a six-part comedy which will premiere April 16 on Amazon Prime.

Ms. Horgan, 50, has made comedies that connect with audiences on both sides of the Atlantic. She and her business partner Clelia Mountford set up their production company Merman in 2015 with a focus on scripted comedy by young women writers and directors. The company produced shows by new talents like Aisling Bea (“This Way Up”), Sarah Kendall (“Frayed”) and Lorna Martin (“Women on the Verge”).

Merman’s first hit was the Emmy-nominated British sitcom “Catastrophe,” which Ms. Horgan co-wrote and starred in with the American actor and comedian Rob Delaney. The Channel 4 show’s popularity attracted the attention of Amazon Prime which streamed it in the U.S. where it also built a following.

Since then Merman has opened offices in Los Angeles and New York, producing shows like “Divorce,” which starred Sarah Jessica Parker in her first repeat role since “Sex and the City.” “A lot of what is brought to us now is from U.S.-based writers,” Ms. Horgan says.

Coming Merman shows include a U.S. remake of Ms. Horgan’s BBC parenting sitcom “Motherland,” which will be co-produced by Paul Feig. There also is “Housebroken,” an animated comedy about neurotic animals in therapy; Ms. Horgan voices an ex-show cat called Tabitha. “Housebroken” premieres May 31 on Fox.