With the rack in the middle position, preheat the oven to 180°C (350°F). Generously butter a tube cake pan with a removable bottom (preferably non-stick).
Place the pan on a baking sheet in case of a leak.
In a bowl, combine the cream, milk, cheese and eggs. Season with salt and pepper. Add the bread and let soak for about 15 minutes, gently stirring it a few times.
Meanwhile, in a skillet over medium-high heat, fry the bacon until barely crisp. Add the ham and brown. Add the green onions and sauté for 1 minute.
Add the tomatoes to the bread mixture and stir to combine. Adjust the seasoning. Pour into the cake pan and bake until golden, about 70 minutes.
Let rest for 15 minutes. Run a thin-bladed knife between the edge of the pan and the pudding. Unmould. Run the knife under the pudding. Using two large spatulas, gently lift the pudding to detach it completely from the pan. Place on a serving platter. (This is best done with two people.)
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.