Arrange your potatoes in a single layer with the cut side down in a 12-inch non-stick skillet. Add water, butter, garlic, thyme and salt and allow to simmer over medium-high heat. Reduce the temp to medium, place a cover and allow the potatoes to simmer until they are just tender. This will take about 15 minutes.
Remove the lid and use a slotted spoon to transfer the garlic to a cutting board; discard the thyme. Increase the heat to medium-high and bring to a vigorous simmer, swirl pan occasionally, until your water evaporates and the butter starts to sizzle. This step will take about 15-20 minutes. When your garlic is cool enough to handle, mince it into a paste. Transfer this garlic paste to a bowl and stir in the lemon juice and pepper.
Continue to cook your potatoes, continuing to swirl the pan frequently, until the butter browns and the cut side of the potatoes turn a spotty brown, an additional 4-6 minutes. Turn off your heat, add the garlic paste mixture and chives and toss to completely coat. Serve immediately.