Clean all vegetables and pat dry. Drain and rinse beans.
Heat oil in a large pot over medium heat.
Chop leeks, using only with and light green parts.
Remove casing from sausage. Add to pan with leeks and cook, stirring occasionally and crumbling the sausage with a wooden spoon until the leeks are tender, about 5 minutes.
Finely chop garlic and add to pan with salt. Stir until fragrant, about 20 seconds.
Add stock, cover and bring to a boil over high heat.
Uncover and cook until the stock is almost evaporated, about 4 minutes.
Slice potatoes into 1/4-inch slices, then add potatoes and broth; cover and bring to a boil.
Stem and chop spinach, and thinly slice scallions. Stir in spinach and scallions and cook, covered, until the potatoes are tender, about 10 minutes.
Remove from heat and stir in beans. Cover and let stand for 1 minute. Divide among six soup bowls and sprinkle each portion with fresh herbs.