Wash the baby red potatoes and cut any larger ones so pieces are roughly 1 to 1 1/4 inches (aim for quarter-size pieces). Place potatoes in a medium pot and cover with cold water by 1 inch. Add 1/2 teaspoon kosher salt. Bring to a simmer over medium-high heat and cook until just tender when pierced with a fork, about 8–10 minutes. Drain and let steam-dry in the colander for 2–3 minutes.

Heat pan

While potatoes cook, heat a large heavy skillet (cast iron or stainless) over medium-high heat. Add the olive oil and butter and let the butter melt and foam but not burn, about 1 minute.

Sear potatoes

Add the drained potatoes in a single layer (work in two batches if necessary). Let them sear, undisturbed, for 3–4 minutes until a golden-brown crust forms. Flip and sear the other side 2–3 minutes.

Aromatics and herbs

Reduce heat to medium. Push potatoes to one side of the pan and add the minced garlic to the oil/butter; cook, stirring, about 30 seconds until fragrant (do not let it brown). Stir potatoes to coat, then add chopped rosemary, thyme, the remaining 1/2 teaspoon kosher salt, and 1 teaspoon black pepper. Toss to combine and cook 1–2 minutes to bloom the herbs.

Finish and brighten

Remove skillet from heat. Stir in lemon zest and chopped parsley to brighten flavors. Taste and adjust seasoning with additional salt or pepper if needed.

Optional finishing

If using, sprinkle grated Parmesan over the hot potatoes so it melts slightly, and finish with a pinch of crushed red pepper flakes for heat. Serve immediately.