Heat oil in a pot over medium heat; cook and stir onion in the hot oil until transparent, 5 to 10 minutes. Stir tomato paste and garlic into onion; cook, stirring quickly, for 1 minute.
Pour in boiling chicken stock.
Stir cardamom, bay leaf, salt, and pepper into onion-stock mixture; bring to a boil.
Add green beans and carrots; return to a boil, reduce heat to medium-low, and simmer until green beans are softened, about 30 minutes.