Make a well in the flour, add eggs and knead until smooth.
Cover with a cotton towel or plastic wrap and set aside to rest for 20 minutes.
Roll out dough into paper-thin sheets (less than 1/16-inch) with a rolling pin or pasta machine.
Cut into 1/2-inch squares with a knife. Bring plenty of lightly salted water to a boil.
Cook 2 or 3 pasta squares at a time for about 30 seconds.
Wet and wring out a cotton towel. Drain and arrange pasta squares on towel and allow to cool.
Clean and chop onion. Heat oil in a pan over medium heat and sauté onion until golden. Add ground meat and brown for a few minutes.
Pour in wine and allow to evaporate. Add canned tomatoes, basil, salt, freshly ground pepper and 2 or 3 spoonfuls of hot water. Cook meat sauce over low heat for at least 30 minutes, until rather thick (if too thick, add a bit of water). Remove from the heat and set aside to cool. Combine 4/5 of the meat sauce with ricotta, a couple of spoonfuls of grated Parmigiano and drained and chopped mozzarella.
Place one spoonful of meat and ricotta filling in the middle of each boiled pasta square and roll up. Line an ovenproof baking dish with parchment paper and butter. Arrange cannelloni in the dish in one layer and cover with remaining meat sauce and grated Parmigiano Reggiano.
Dot with butter and cook in a preheated 350°F oven for 15 - 20 minutes.