Heat oil in a large pot over medium-high heat and add sliced kielbasa. Cook until nicely browned to deepen the smoky flavor. Remove sausage and set aside while preparing the base.
In the same pot, melt butter and add onions, carrots, garlic, salt, and pepper. Cook until vegetables soften and become aromatic. This stage builds the soup’s flavor foundation.
Sprinkle flour over the vegetables and stir well for about one minute. Cooking the flour removes raw flavor and helps thicken the soup smoothly.
Slowly pour in chicken broth and milk while stirring constantly. Add Worcestershire sauce and bring mixture to a gentle simmer so flavors begin blending.
Return browned kielbasa to the pot along with drained beans. Stir well so everything is coated in the creamy broth.
Reduce heat and simmer gently for 15–20 minutes. The soup thickens and flavors fully develop during this final step.