Cut the Yukon Gold potatoes into 2-inch chunks, which ensures even cooking throughout—smaller pieces cook faster but can become waterlogged and mealy. Bring a large pot of salted water to a rolling boil, then add the potato chunks. The water should cover the potatoes by about an inch. Maintain a steady boil and cook for 20-25 minutes until the potatoes are completely fork-tender and easily fall apart when pierced. This is your foundation for creamy mashed potatoes, so don't rush this step.
While the potatoes are cooking, warm the olive oil in a small skillet over medium heat. Add the minced garlic and cook for just 1-2 minutes until fragrant but not browned—burnt garlic becomes bitter and will ruin your dish. Pour in the vegetable broth to combine with the garlic oil, then remove from heat. I like to use extra virgin olive oil here because it adds a subtle richness that compensates beautifully for the missing dairy.
Drain the cooked potatoes thoroughly in a colander—excess water left in the potatoes will make them thin and watery instead of creamy. Return the hot drained potatoes to the empty pot immediately (the residual heat keeps everything warm). Pour in the garlic-broth mixture from Step 2, then add the salt and black pepper. Start mashing right away while everything is hot, as warm potatoes absorb the flavorings much better than cooled potatoes.
Using a potato masher, break down the potatoes with firm, steady pressure until you reach your preferred texture—I recommend leaving them slightly chunky for a rustic feel, but you can mash longer for a completely smooth consistency. The broth provides all the moisture you need for creaminess without any dairy. Taste and adjust seasoning if needed, then serve immediately while hot. Mashed potatoes lose their appeal quickly as they cool, so get them to the table while they're at their best.