Vodka and pierogies are pretty natural fits for Great Comet.
Waffles for Oslo.
I am a firm believer in serendipity- all the random pieces coming together in one wonderful moment, when suddenly you see what their purpose was all along.
Natasha, Pierre & the Great Comet of 1812... vodka and pierogies. For nonalcoholic and nonsavory options you could have tea and some kind of small petit-fours or cookies for Natasha's visit to her future in-laws.
Amelie... goldfish crackers, aquarium cookies, red wine, heart-shaped desserts
Falsettos... hors d'oeuvres inspired by Cordelia's menu for the bar mitzvah
Hello Dolly... I only know the movie but food is mentioned
The Present... birthday cake
Holiday Inn... any Christmas, Thanksgiving, 4th of July, etc. foods you feel like making
We're combining several shows by having Ben Platt-breads, which are flatbread pizzas with ground sausage (Groundhog Day), vodka sauce (Natasha et al), and Canadian cheese (Come From Away). Plus Vietnamese spring rolls (Miss Saigon). And to drink, hot Bette-red rum.
I'm sending pictures of the most amazing trees/You'll be obsessed with all my forest expertise
Since a lot of people are suggesting puns instead of foods seen or referenced in the Tony nominated show I thought I would throw out some decorating tips. You probably don't have a food-safe printer... like the kind they use for cake. But if you're serving anything with skewers, you can print pictures of the performers or show marquis, etc., attach it to a bit of cardboard backing and glue it to the top. Same idea with drink stirrers, coasters, etc. Some low-level craftiness if anyone is so inclined. :)