Martha Stewart's Granddaughter Jude Celebrates Her First Birthday

Some first birthday parties include homemade birthday cakes and photos of babies with frosting all over their faces – but few babies have Martha Stewart for a grandmother.

Last Thursday, Stewart and her daughter Alexis hosted an intimate celebration at Perry St., a restaurant in New York, to toast Alexis’s daughter Jude’s first birthday.

Alexis Stewart Is a Mom Again

It s a boy for Alexis Stewart!

Martha Stewart’s daughter welcomed her second child, a son named Truman, who was born via surrogate on Tuesday, March 6, PEOPLE confirms exclusively.

Truman arrived just in time to help big sister Jude celebrate her first birthday on Thursday.

Martha Stewart Says Daughter's Tell-All Book Is 'Hilarious'

Martha Stewart certainly is not offended by the fact her daughter, Alexis Stewart, is unleashing a tell-all about growing up under the heavy thumb of her mother.

Not only is Stewart’s Blackberry buzzing about the book – “I get a little ‘ping ping’ like every five minutes,” says the domestic diva, 70 – but, she says, “I got an advanced copy and I actually read the book oh, maybe about a month or a month and a half ago. I didn’t know that it was even coming.”

Martha Stewart's Daughter Rips Into Her Mom – and Childhood – in Tell-All Book

Was über-hostess and domestic darling Martha Stewart more like Mommie Dearest as a parent?

Her daughter Alexis, 46, levies some harsh claims in her new book, Whateverland: Learning to Live Here, co-authored with Jennifer Koppelman Hutt.

Martha Stewart Is a Grandma!

Martha Stewart’s only child, Alexis, has welcomed a daughter of her own.

The baby girl, Jude, was born via gestational carrier on Tuesday.

Though the entertaining guru is surely glad to have a granddaughter, don’t expect her to be a typical grandmother. “Martha is going to be called, ‘Martha,’” Alexis announced on her radio show, Whatever with Alexis & Jennifer. “She seemed to have no problem with it. … I was like, ‘Do you really want to be ‘grandma’? I don’t like the term grandma!”

Alexis Stewart Continues Fertility Treatments

Even though her eggs are “dry and crusty” (as she called them), Alexis Stewart is determined to get pregnant – so determined, she spends $28,000 a month on fertility treatments.

Stewart, 42, started the difficult process last year, and opened up to PEOPLE in July about how lucky she is to be able to afford the high-tech procedures and special treatments. On Tuesday, she talked to Oprah Winfrey about the emotionally and financially draining process.