Filling: In a 10- to 12-inch ovenproof frying pan over high heat, stir butter, onion, and garlic frequently until limp but not browned, 5 to 7 minutes.
As onion cooks, cut chicken and veal into about 2-inch chunks. Stir into onion mixture. Bake in a 400° oven just until meat is no longer pink in center (cut to test), about 15 minutes.
Let mixture cool, then add ricotta. Coarsely purée mixture in a food processor (or grind through a food chopper). Add parmesan, egg yolks, nutmeg, and salt to taste, mixing well.
Sauce: In a 4- to 5-quart pan over high heat, combine butter and shallots and stir often until shallots are limp, about 2 minutes. Add flour and stir until bubbling. Off the heat, whisk in milk and broth. Stir often over medium heat until reduced to 1 1/3 cups, about 25 minutes. Remove from heat.
Drain tomatoes; save juice for other uses. Add tomatoes and the chopped basil to sauce.
Pasta: Mound 1/8 of the filling (about 6 tablespoons) evenly along 1 side of each egg roll wrapper. Roll each wrapper to enclose the filling. Set rolled cannelloni, seam down and slightly apart, in 2 lightly oiled 3-quart casseroles (about 9 by 13 in., and at least 2 in. deep).
Cut teleme cheese into thin pieces and lay pieces onto cannelloni so that each top is completely covered. Spoon the sauce around the cannelloni, adding an equal amount to each casserole. If making ahead, cover and chill up to 1 day.
Bake, uncovered, in a 425° oven until sauce bubbles and cannelloni are hot in the center, 10 to 15 minutes (the same time if chilled). Garnish casserole with basil sprigs. Use a wide spatula to transfer a cannelloni to each plate, spooning sauce around portions. Add salt to taste.