Arrange the beets in a single layer in a large skillet. Add the water and a pinch of salt, then bring to a simmer over medium-high heat. Reduce the heat to low, cover the skillet, and cook until a paring knife enters the beets with no resistance, about 40 to 45 minutes.

Transfer the beets to a plate. Once they are cool enough to handle, use a paper towel to rub the skins away from the flesh—they should slip off easily. Cut the peeled beets into thick wedges.

Increase the heat to medium-high and stir the vinegar and brown sugar into the braising liquid remaining in the skillet. Simmer steadily until the liquid reduces to a thick, glossy syrup.

Add the beet wedges and shallot to the syrup in the skillet. Cook for a few minutes, stirring occasionally, until the beets are heated through and the glaze is clinging to the wedges.

Remove the skillet from the heat and fold in the lemon zest, almonds, mint, and thyme. Season with salt and pepper to taste and serve warm, or at room temperature.