The culprits smashed a window at Pride & Provenance, next door to The Piece Hall, and stole £800-worth of goods in the early hours of October 5.
Owners Melanie and James Thompson say it is the second break-in in 18 months.
"We're pretty devastated," said Melanie, added that it had been tough enough having to run the business through the challenges of the pandemic which have included having to shut during lockdowns.
"It just makes you feel sick," she said.
The first break-in happened in March last year, at the beginning of the pandemic, when the culprits smashed a different window.
The couple posted on social media: "During the early hours of this morning (Oct 5) our beautiful Pride & Provenance was broken into, entered and approximately £800 retail value of goods stolen and other items damaged.
"The police have been with us most of the morning and some of our fantastic team have helped clear the mess up this afternoon.
"Please may we ask you all to continue to support local, shop or dine with us when you can or even just liking or sharing our posts helps our family business.
"Two break ins in the space of 18 months is heartbreaking and very costly for a small business.
"Thanks as always for your support."
Pride & Provenance reopened today (Oct 6).
Last month the establishment, which opened in 2018, was selected from thousands across the country as one of the top 15 indie restaurants in the country by www.coffeefriend.co.uk based on its TripAdvisor reviews, boasting a 5/5 rating with a 96 per cent excellent review ratio.
Anyone with information about the break-in, which happened between 2am and 2.10am on October 5, should call police on 101.
Information can also be passed on anonymously via Crimestoppers on 0800 555111.