The phrase "thick pudding" refers to a type of dessert that is very dense, creamy, and not runny. It means the pudding has a lot of substance and is less watery in its texture. Full definition
The soup, as prepared per the recipe, came out as a very thick pudding. (epicurious.com)
2 Place the pork in a medium bowl and stir in enough broth, 1 tablespoon at a time, until the mixture has the consistency of thick pudding. (styleathome.com)
I followed the directions as written, but mine turned out more of the consistency of soft tofu or a very thick pudding. (cookingwithplants.com)