Season the beef cubes with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Add the beef cubes in batches and brown on all sides, about 3-4 minutes per batch. Transfer browned beef to the crock pot.
In the same skillet, add sliced mushrooms and cook for 5 minutes until softened and browned. Add chopped onion and cook for another 3 minutes until translucent.
Add minced garlic and cook for 1 minute until fragrant.
Stir in tomato paste and cook for 1 minute.
Pour in Marsala wine and beef broth, scraping the bottom of the skillet to loosen browned bits.
Add dried thyme and rosemary. Bring the mixture to a simmer and cook for 3-4 minutes to reduce slightly.
Pour the mushroom and wine mixture over the beef in the crock pot.
Cover and cook on low for 6 hours, or until the beef is tender.
About 30 minutes before serving, melt butter in a small bowl and whisk in flour until smooth to create a slurry.
Stir the slurry into the crock pot to thicken the sauce. Cover and cook on high for 30 minutes.
Taste and adjust seasoning with salt and pepper if needed.
Sprinkle chopped fresh parsley over the beef marsala before serving.