Heat the vegetable oil in a large pot over medium-high heat. Add the pork cubes and brown them on all sides, about 6 to 8 minutes total. Remove the pork and set it aside.
Lower the heat to medium. Add the diced onion to the same pot and cook until it softens, about 5 minutes. Stir in the minced garlic and cook for 1 minute more.
Add the sliced bell peppers and cook for 3 minutes until they begin to soften. Sprinkle in the Hungarian paprika and stir quickly for 30 seconds to avoid burning it.
Pour in the crushed tomatoes and chicken broth. Add the browned pork back to the pot along with the salt and black pepper. Stir everything together.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 1 hour, stirring occasionally, until the pork is tender and the broth has thickened slightly.