Prepare the potatoes first. Peel the russet potatoes and cut them into evenly sized chunks so they cook at the same rate.
Place the potato chunks in a large pot, cover with cold water by about an inch, and add a pinch of salt. Bring to a gentle boil over medium-high heat.
Reduce the heat to maintain a steady simmer and cook the potatoes for 15–20 minutes, or until they are very tender when pierced with a fork.
While the potatoes cook, thinly slice the beef sirloin into strips, cutting against the grain for tenderness. Pat the strips dry with paper towels to help them brown well.
Season the sliced beef lightly with a pinch of salt and black pepper, then set aside while you prepare the pan for browning.
Heat the olive oil and 1 tablespoon of the unsalted butter in a large skillet over medium-high heat until the butter is melted and the fat is shimmering.
Add about half of the beef strips in a single layer and sear for 1–2 minutes per side, just until browned but not fully cooked through. Transfer the browned beef to a plate.
Repeat with the remaining beef strips, adding a little more oil if needed, and transfer all browned beef to the plate, leaving any browned bits in the skillet.
Reduce the heat to medium, add the remaining 1 tablespoon of unsalted butter to the skillet, and let it melt into the browned bits.
Add the sliced yellow onion to the skillet and cook, stirring occasionally, for 4–5 minutes until softened and lightly golden.
Stir in the minced garlic and cook for about 30 seconds, just until fragrant, being careful not to let it burn.
Add the sliced mushrooms to the skillet and cook for 5–6 minutes, stirring occasionally, until they release their moisture and turn golden in spots.
Sprinkle the all-purpose flour evenly over the onion and mushroom mixture, stirring well to coat the vegetables and cook the flour for about 1 minute.
Gradually pour in the beef broth while stirring, scraping up any browned bits from the bottom of the skillet to build flavor.
Stir in the Worcestershire sauce, Dijon mustard, paprika, 1/2 teaspoon of salt, and 1/2 teaspoon of black pepper, mixing until the sauce is smooth.
Bring the sauce to a gentle simmer and cook for 3–4 minutes, stirring occasionally, until it slightly thickens and becomes glossy.
Return the browned beef and any accumulated juices to the skillet, stirring to coat the beef in the sauce, and simmer on low heat for 3–5 minutes until the beef is just cooked through.
Turn the heat to low and let the stroganoff cool slightly for a minute, then stir in the sour cream until fully blended and creamy. Avoid boiling after adding sour cream to prevent curdling.
Taste the beef stroganoff and adjust the seasoning with additional salt and black pepper if needed, then stir in the chopped fresh parsley.
When the potatoes are very tender, drain them well and return them to the warm pot, letting excess steam escape for a minute so they are not watery.
Add the 4 tablespoons of unsalted butter for mashed potatoes to the hot potatoes and mash until the butter is mostly melted and incorporated.
Pour in the warmed whole milk a little at a time while mashing, until the potatoes reach your desired creamy consistency.
Season the mashed potatoes with 3/4 teaspoon of salt and 1/4 teaspoon of black pepper, then continue mashing or whipping until smooth and fluffy.
To serve, spoon a generous bed of mashed potatoes onto each plate and ladle the creamy beef stroganoff over the top, making sure each portion gets plenty of sauce and mushrooms.
Finish each plate with a light sprinkle of the remaining chopped fresh parsley if desired, and serve the beef stroganoff and mashed potatoes hot.