Turn broiler to high and set rack 4 inches (10 cm) below it.
Heat oil in a large pot over medium heat. When oil is hot, add sausages and cook slowly, stirring occasionally, until no longer pink, 5 to 10 minutes.
Raise heat to medium-high and add onion and garlic. Cook, stirring often, until the sausages sizzle and brown and the vegetables soften and turn golden, 3 to 5 minutes.
Stir in thyme, pinch of salt and cayenne. Add wine and continue to cook, scraping up any browned bits from the bottom of the pot, until the liquid is reduced by half, 2 to 3 minutes.
Add tomatoes and half the beans, and bring to a boil. Reduce heat so mixture bubbles gently. Cook, uncovered, stirring occasionally, until mixture thickens and darkens, 10 to 15 minutes.
If adding a crumb crust, tear bread into bite-size pieces, place on a rimmed baking sheet, and broil in preheated broiler until crisp and browned, about 2 to 3 minutes, shaking the baking sheet to turn bread. Remove pan from broiler and cool.
Add remaining beans to the pot. If the mixture looks too thick, add more wine or water, 1/4 cup (60 mL) at a time. Heat for a few minutes, stirring occasionally.
Adjust seasonings and serve, topped with the bread (if using) and a drizzle of olive oil.