Heat large pot over medium-high heat and add butter. Once melted and sizzling, add cubed steak in single layer. Cook until browned on all sides, about 4-5 minutes, turning occasionally. Remove and set aside.
In same pot, add chopped onion and minced garlic. Sauté 2-3 minutes until softened and fragrant, stirring frequently.
Add diced potatoes, beef broth, salt, pepper, and paprika. Stir well, scraping up brown bits from bottom of pot.
Bring to boil, then reduce heat to medium-low and simmer 15-20 minutes until potatoes are fork-tender, stirring occasionally.
Return browned steak to pot along with heavy cream and milk. Stir gently to distribute steak evenly.
Simmer 5-7 minutes to heat through and meld flavors. Cream should be steaming but not boiling rapidly.
If using fresh thyme, stir in during last few minutes of cooking for aromatic quality.
Taste and adjust seasoning as needed with more salt, pepper, or paprika.
Remove from heat and let rest 1-2 minutes. Ladle into bowls and garnish with chopped parsley.
Notes
Best steaks: top round or chuck roast for juicy, flavorful, tender beef. Sirloin or rib-eye work but are more expensive.
Best potatoes: Russet, Yukon Gold, or red potatoes hold shape well and provide right balance of creaminess.
Use whole milk and heavy cream for creamiest texture. Whole milk can substitute heavy cream but texture may not be as thick.
Not recommended for freezing. Potatoes and dairy-based broth may become grainy. Store refrigerated up to 3-4 days.