Place the beets cut side down in a single layer in an 11-inch straight-sided sauté pan or Dutch oven. Add the water and salt, then bring to a simmer over high heat. Reduce the heat to low, cover, and simmer for 45 to 50 minutes until the beets are tender and a paring knife meets no resistance when inserted.

Transfer the beets to a cutting board. Increase the heat to medium-high and reduce the cooking liquid, stirring occasionally, until the pan is almost dry, about 5 to 6 minutes. Add the vinegar and sugar, return to a boil, and cook while stirring constantly with a heat-resistant spatula until the glaze is thick enough to leave a wide trail when the spatula is dragged through it.

Rub off the beet skins with a paper towel once they are cool enough to handle, then cut them into half-inch wedges. Add the beets, shallot, lemon zest, salt, and pepper to the glaze and toss to coat thoroughly. Transfer to a platter, sprinkle with the toasted almonds, mint, and thyme, and serve warm.