Heat the olive oil in a large Dutch oven over medium-high heat. Add the pork cubes and brown them on all sides, about 6 to 8 minutes. Remove the pork and set it aside.
Add the mushrooms and pearl onions to the pot. Cook for 5 minutes until the mushrooms start to brown and the onions soften slightly. Stir in the garlic and cook for 1 minute more.
Return the pork to the pot. Stir in the tomato paste and cook for 2 minutes. Add the crushed tomatoes, chicken broth, thyme, and bay leaf. Season with salt and black pepper.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 1 hour and 15 minutes, stirring occasionally, until the pork is tender.
Remove the bay leaf. Sprinkle with fresh parsley before serving.