Vanessa Hudgens is super proud to have a bun in the oven ... because she was showing off her growing baby bump at brunch with her family.

Check out these pics and vids we obtained of Vanessa at The Henry in Phoenix ... she's got her shirt above her stomach and it looks like she's pretty far along in her pregnancy. TMZ.com

Vanessa broke bread Wednesday morning with her husband, former MLB shortstop Cole Tucker , and their one-year-old.

Unclear when Vanessa is due this time around, but she announced the pregnancy back in July ... and at the time, she already had a baby bump in her maternity photos. TMZ.com

In other words, this baby could be brought into the world very soon!!!

The "High School Musical" alum was first linked to Cole in November 2020 and they got engaged in Febru

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