Cook the rice according to the directions on the package in salted water.
In a pot over medium heat, brown the ground beef, breaking it up into smaller pieces. Add the onion and mushrooms; season with salt and pepper. Cook until the vegetable start to soften. Mix in the flour and cook for 2 minutes.
Add the broth and thyme, cover with a lid, and bring to a simmer for about 20 minutes to build flavor. Stir in the cream and simmer for 5 minutes longer. Taste and adjust the seasoning with salt.
Remove the thyme sprigs, serve over rice with bread. Garnish with parsley.