Cut the Kielbasa up into small slices and finely chop the garlic. Chop the parsley. Halve the tomatoes.
Heat a heavy-bottomed pan over medium-high heat for three or four minutes. When the pan is hot, add the oil and swirl to coat the pan.
When the oil shimmers, add the sausage and sauté until lightly browned. Add the drained beans, the chicken stock, garlic, tomatoes and half the parsley to the pan. Season to taste with salt and pepper.
Simmer gently for at least thirty minutes so the flavors can meld.
About five minutes before serving, add the other half of the chopped parsley, reserving just a bit for garnish.
To serve, ladle into bowls and sprinkle with a little fresh parsley.