In a large saucepan or Dutch oven, heat 1 tablespoon (15 ml / 0.5 fl oz) of the olive oil over medium-high heat.
Add the chopped carrots and onion, and sauté for 3 minutes until they begin to soften and become fragrant.
Pour in the vegetable broth, add the rinsed beans and the crushed Italian seasoning.
Bring the mixture to a boil, then reduce the heat to maintain a steady simmer.
Cook, uncovered, for 8 minutes, stirring occasionally.
Gently press a potato masher or the back of a fork into the soup a few times to slightly mash some of the beans. This creates a wonderfully creamy texture.
While the soup simmers, heat the remaining 2 tablespoons (30 ml / 1 fl oz) of olive oil in a large skillet over medium-high heat.
Add the entire package of baby spinach and toss continuously with tongs for 1-2 minutes, just until it's perfectly wilted.
Remove from the heat immediately to retain its vibrant green color.
To serve, ladle the hot soup into bowls.
Top each serving with a generous portion of the wilted spinach, a sprinkle of freshly cracked black pepper, and serve alongside soft cracker bread for dipping, if desired.
