Cut the yellow potatoes into 1-inch chunks to ensure even cooking throughout—this is crucial for avoiding mushy edges and undercooked centers. Bring a large pot of water to a rolling boil, then add the salt, potato chunks, and smashed garlic cloves. The salt seasons the potatoes from the inside out as they cook. Simmer for about 15 minutes until the potatoes are completely tender and easily pierced with a fork, then immediately drain, reserving 1 cup of the starchy cooking water—this water is liquid gold for getting the right creamy consistency.

Return the drained potatoes and garlic to the hot pot (the residual heat helps everything mash smoothly). Add the extra-virgin olive oil and dried thyme, then begin mashing with a potato ricer or masher until you reach your preferred texture—I prefer leaving them slightly chunky for a rustic feel, but mash to your liking. Gradually add the reserved cooking water a little at a time while mashing, stirring gently between additions until you reach the exact consistency you want. The starch in the cooking water creates a silky, luxurious texture that regular milk or cream can't quite achieve.

Taste the mashed potatoes and adjust seasoning as needed—remember that salt was added during cooking, so you may only need a small adjustment. Transfer to a serving dish and finish with a generous grind of fresh black pepper and fresh thyme if you have it available. Fresh thyme adds a bright, aromatic note that complements the rich olive oil beautifully.