A "generous tablespoon" refers to a larger amount than a regular tablespoon. It means using more than the usual amount of an ingredient when measuring or adding it to a recipe or dish. Full definition
If I'm making vegetable or lentil soup, I'll stir in a few generous tablespoons of sauce into it to enrich it and give it that depth and complexity that tomato provides. (landsandflavors.com)
When the oil is hot enough, carefully place generous tablespoons full of the potato mixture into the skillet. (healthimpactnews.com)
Using two spoons or a cookie scoop, spoon generous tablespoon size balls of dough onto the sugar set aside for rolling. (strawberriesforsupper.com)