Heat oil in a Dutch oven over medium-high heat. Once hot, add beef in one even layer, cooking until the meet is only slightly pink on top. Remove from pan and set aside.
Add diced onion, carrot, celery, and garlic to hot pan and reduce heat to medium. Cook until the vegetables soften, about 5 minutes. Add tomato paste and stir until it combines with the vegetables. Cook for 30 seconds. Add broth, beef, parsley, thyme, bay leaf, and beef and stir together. Bring mixture to a boil and then reduce to a simmer. Cover and cook for 90 minutes.
When the 90 minutes are almost done, it's time to create the roux, which will thicken the soup. To do this, melt the butter in a small skillet over medium heat. Once melted, add te flour and whisk together. Continue whisking until the mixture starts to turn golden brown. Remove from heat and slowly pour into stew and stir together. Cook for another 3 minutes.
Finish off the stew by adding the frozen peas. Let them cook through and then serve the stew. It's best over mashed potatoes.