Preheat your oven to 375°F (190°C).
Sauté the diced vegetables in a bit of oil until soft, about 5 minutes.
Remove vegetables from heat and combine with the bread in a large bowl, adding herbs, salt, and pepper.
Pour in the vegetable broth and cheese; mix until combined.
Lay out slices of bread and fill them with the stuffing mixture, then roll them up tightly.
Place the roll-ups seam-side down in a greased baking dish, and cover with foil.
Bake for 25-30 minutes until heated through.
While baking, prepare the creamy gravy by whisking together the flour and heavy cream in a saucepan over low heat.
Gradually add broth to the cream mixture until you achieve your desired thickness, cooking until bubbly.
Serve the roll-ups hot, drizzled with creamy gravy.