Place halved baby potatoes in a large microwave-safe bowl with 2 tablespoons water, cover with plastic wrap, and microwave on high for 5-6 minutes until just fork-tender. Drain well and pat very dry.
In a large cast-iron skillet over medium-high heat, heat 1 tablespoon olive oil and 1 tablespoon butter until shimmering. Add potatoes cut-side down in a single layer. Cook undisturbed for 4-5 minutes until deeply golden and crisp. Flip and cook 2-3 more minutes. Transfer to a plate.
Pat steak bites dry with paper towels. Toss with salt, pepper, smoked paprika, and red pepper flakes (if using). In the same skillet over high heat, add remaining 1 tablespoon olive oil. Add steak in a single layer; sear for 2-3 minutes per side, until browned and an instant-read thermometer inserted into the thickest piece reads 145°F (63°C) for safe consumption, working in batches. Transfer steak to a plate.
Reduce heat to low. Add remaining 3 tablespoons butter and minced garlic to the skillet. Cook, stirring constantly, for 30-60 seconds until fragrant but not browned. Stir in thyme leaves.
Return steak and potatoes to the skillet, toss gently in the garlic butter to coat and warm through for 1 minute. Sprinkle with fresh parsley and serve immediately.