In a large bowl, combine the ground beef, breadcrumbs, onion, tomato paste, garlic, egg, salt, and pepper. Using your hands, mix well and form 4 equally-sized patties.
Heat a large frying pan over medium heat and add the 1 teaspoon of olive oil to prevent sticking. When the oil is heated and shimmering, add the patties and brown, about 2-3 minutes on each side. You may need to do this in batches to avoid overcrowding. Remove the patties and set them aside.
Turn your Instant Pot to saute mode and heat the 2 tablespoons of olive oil. Add mushrooms and onion and saute until the onions are slightly translucent, about 3-4 minutes.
Add garlic and cook for 1-2 minutes until a light golden brown.
Add dijon mustard, thyme, brown sugar, salt, and black pepper. Stir to combine and cook until fragrant, about 1 minute.
Turn saute mode off. Pour in half of the broth, stir, and place the patties on top. Seal the Instant Pot and cook on high pressure for 10 minutes. Quick release the pressure once the time is up.
Remove the patties and set them aside.
In a small bowl, whisk the remaining broth, cornstarch, and heavy whipping cream together.
Turn on saute mode. Add the broth/cornstarch/cream slurry. Cook for 2-4 minutes until thickened, whisking constantly.
Pour the gravy over the patties. Garnish with parsley and serve.