The pair looked "very cozy and romantic" during dinner at L.A. eatery Animal, a source tells PEOPLE

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Gwyneth Paltrow and producer Brad Falchuk took their romance tableside on Tuesday.

The actress, 42, and the Glee co-creator, 44, dined at the L.A. restaurant Animal, which featured a barbecue-themed menu on Tuesday of pig ears, veal tongue and fried rabbit legs.

“They were sitting together, very cozy and romantic,” says the observer at the eatery. “He was totally rapt by everything she was saying. They were totally on a date.”

The dinner followed Paltrow’s announcement on April 9 that she had accepted the Food Bank for New York City challenge to bring attention to the struggles faced by families that live on the Supplemental Nutrition Assistance Program (SNAP), or food stamps, which Congress has slashed twice during the past 18 months.

It’s unclear whether Paltrow is still participating in the campaign, which involves living off a $29 food-stamp budget for a week, or $1.38 per meal.

The Oscar winner accepted the challenge from friend and chef Mario Batali, who posed it to several of his celebrity pals, including Sting and Deborah Harry.

“We’re walking in their shoes to see how far we get,” Paltrow Tweeted on April 9. She also donated to Food Bank for New York City, having long supported the organization behind the challenge, which provides food for millions of needy New Yorkers.

More than 47 million people nationwide are on food stamps, according to The Washington Post, with the average weekly allowance amounting to $29 in some states. SNAP recipients (about 45 percent of whom are reportedly children under 18) say they often run out by the third week of every month.

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