Trim the cauliflower and carefully cut it into 2-inch-long, 1-1/2-inch-wide florets; discard any small crumbly pieces. Measure 6 cups of the florets and save any extra for another use. In a small bowl, whisk together the honey and vinegar.
Heat 3 Tbs. of the olive oil in a 12-inch skillet over medium heat. Add the 6 cups of cauliflower florets, sprinkle with 1 tsp. kosher salt, and toss gently with tongs to coat with the hot oil. Arrange the cauliflower in one layer and let cook undisturbed until the bottoms are lightly browned, about 3 minutes. Using tongs, flip each floret to an unbrowned side, and add another tablespoon of oil if the pan seems dry. Let cook undisturbed again for about 3 minutes to lightly brown that side. Repeat twice more for a total of about 6 more minutes, or until all sides of the cauliflower are spotted with golden brown. The stems of the florets will still be fairly firm, but the tops will be getting tender.
Raise the heat to medium high and add the honey-vinegar mixture and thyme. Toss to coat the cauliflower and continue to toss gently until the liquid reduces to a glaze on the florets, about 3 minutes. Remove the pan from the heat, taste a floret, and add a little more salt, if necessary. Squeeze the lemon quarter over the cauliflower, add the toasted almonds, and toss to combine. Serve right away, or let sit for up to 30 minutes and serve barely warm.