“I do think that I am holding, you know, a little bit more close to my heart on certain aspects of my relationship with Pete, and it feels good just to know that, like,

Late nite snack," Kardashian, 41, captioned the images of her and Davidson, 28, embracing in the corner booth.

The pair dined at Jon & Vinny's, a popular Italian restaurant in L.A., with friends and family last Thursday after the red carpet premiere of her new

Joining the happy couple were Kourtney Kardashian and Travis Barker as well as longtime friends Jonathan Cheban and Tracy and Roy Romulus.

"Late nite snack," Kim wrote on her Instagram Stories at the time, tagging the restaurant and those around the table.

Kardashian's PDA post on Monday marks the second time she shared photos of her and Davidson after she finally made their relationship Instagram official last month.