Prepare the ingredients by thinly slicing the beef sirloin into strips, slicing the onion and mushrooms, mincing the garlic, and chopping the fresh parsley. Cook the pasta, rice, or egg-free noodles according to package directions, then drain and set aside.

Warm the olive oil and dairy-free butter or margarine in a large skillet over medium-high heat until the fat is hot and shimmering.

Add the sliced beef sirloin to the hot skillet in a single layer, season lightly with a pinch of the salt and black pepper, and sear for 2 to 3 minutes, just until browned on the outside but still slightly pink inside. Transfer the browned beef to a plate and set aside, leaving any juices in the pan.

Reduce the heat to medium, then add the sliced onion to the same skillet. Cook, stirring occasionally, for about 4 to 5 minutes, until the onion softens and begins to turn golden at the edges.

Add the sliced mushrooms to the skillet with the onion. Cook for another 5 to 6 minutes, stirring now and then, until the mushrooms release their moisture and become browned and tender.

Stir in the minced garlic and cook for 30 seconds to 1 minute, just until fragrant, being careful not to let it brown too much.

Sprinkle the all-purpose flour evenly over the onion and mushroom mixture. Stir well to coat the vegetables in the flour, and cook for 1 to 2 minutes to remove the raw flour taste.

Slowly pour the beef broth into the skillet while stirring constantly to avoid lumps, scraping up any browned bits from the bottom of the pan as you go.

Add the canned full-fat coconut milk, Dijon mustard, lemon juice, paprika, the remaining salt, and the remaining black pepper to the skillet. Stir until everything is well combined and the sauce looks smooth.

Bring the sauce to a gentle simmer over medium heat and cook for 4 to 5 minutes, stirring occasionally, until it thickens into a creamy consistency that coats the back of a spoon.

Return the seared beef and any accumulated juices on the plate to the skillet. Stir to coat the beef in the sauce, then simmer gently for 3 to 4 minutes, just until the beef is heated through and cooked to your desired doneness.

Taste the sauce and adjust the seasoning with a little more salt or black pepper if needed.

To serve, spoon the dairy-free beef stroganoff over the cooked pasta, rice, or egg-free noodles. Sprinkle the chopped fresh parsley over the top as a garnish.

Serve the dish hot, enjoying the creamy dairy-free sauce, tender beef, and savory mushrooms together while everything is warm and comforting.