The engaged (and pregnant!) singer and her mom dine on N.Y.C.'s best barbecue and Italian

While Ashlee Simpson has not yet officially confirmed her pregnancy, she’s certainly eating with gusto.

After her MTV TRL taping Tuesday, the newly engaged singer joined her mother, bodyguard and three friends for lunch at Virgil’s BBQ in New York City’s Times Square.

The youngest Simpson, 23, dressed in a long, blue pea coat and leggings, scarfed down a brisket melt – grilled onions and cheddar cheese on grilled rye bread – with French fries. That evening, Simpson and her mother were spotted dining at New York Italian eatery Da Umberto.

Simpson, who revealed her engagement to Fall Out Boy bassist Pete Wentz, 28, last week, is in the Big Apple promoting her album Bittersweet World.

On Monday a source confirmed to PEOPLE that the two are expecting and plan to wed in May in La Jolla, Calif., at a friend’s house.