Bring a large pot of salted water to boil and cook egg noodles according to package directions. Drain and set aside, reserving one cup of pasta water for sauce adjustments.
Pat beef strips completely dry with paper towels—moisture prevents proper browning and searing. Season generously with salt and pepper on both sides before cooking.
Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Working in batches, sear beef strips for 2-3 minutes per side until deeply browned, then transfer to a plate.
Reduce heat to medium and add butter to the same pot. Sauté diced onions for 4 minutes until softened, then add sliced mushrooms and cook for 5 minutes until golden. This stroganoff recipe depends on proper mushroom browning to develop rich umami flavors.
Add minced garlic and tomato paste, stirring constantly for one minute until fragrant. Pour in beef broth, scraping up browned bits from the pot bottom with a wooden spoon.
Return beef to the pot along with paprika and thyme. Simmer for 8 minutes, allowing flavors to meld and beef to finish cooking through completely.
Mix cornstarch with water to create a slurry, then stir into the simmering sauce. Cook for two minutes until it thickens noticeably, then remove from heat.
Whisk sour cream and Dijon mustard together in a small bowl, then slowly stir into the beef stroganoff. Add cooked noodles and toss gently to combine without breaking them.