“They already have been through so much when they get here — they shouldn’t have to get used to another new thing right away,” said Ulla Farmer, a member of the Rutgers congregation, who made the first dinner for the Anjari-Abdulhamid family even though she had never tasted Syrian food. (She immigrated from Finland in 1963.)

Working from online recipes and grocery lists, Ms. Farmer cooked a dinner of lamb stew and cracked wheat, and stocked the family’s new kitchen with key ingredients like tahini, yogurt, cucumbers and rice.

“The culturally appropriate hot meal is simply the best federal regulation of all time,” said Chris George, executive director of Integrated Refugees & Immigrants Services, a New Haven agency that has resettled more than 6,000 refugees in Connecticut since 1982.

Mr. George is a passionate advocate for what he calls the CAHM (he even wrote a song about it), and his enthusiasm has percolated through the agency. For Congolese and Rwandan arrivals, volunteers have made chicken moambe, a braise with tomato, onion, peanut butter and rich red palm oil, a basic ingredient in those countries and for many, the taste of home. For an Eritrean mother and children, an Ethiopian family who had arrived earlier supplied a meal with injera, the soft, spongy flatbread that is a staple in both countries.

Fereshteh Ganjavi, who arrived from Afghanistan in 2013 and now works at Integrated Refugees, said the meal is particularly powerful for refugees who arrive after years of exile from their home country. Her welcome dinner included a traditional pulao of lamb and rice with raisins, and green tea spiced with saffron and cardamom, a brew specific to the mountainous Hindu Kush region that stretches across northern Afghanistan and Pakistan. “We were living in a camp before entering the U.S., and I had almost forgotten the taste of our own food,” she said.