Preheat the oven to 425°F (220°C). Line a large rimmed baking sheet with parchment paper.
Prepare the carrots: if using large carrots, halve them lengthwise so all pieces are roughly the same thickness; leave small baby carrots whole. Trim the tops to about 1 inch, if you like.
Roast: toss the carrots with the olive oil, 1/2 teaspoon salt, and the black pepper. Spread in a single layer on the prepared baking sheet, leaving space between pieces. Roast for 22 to 25 minutes, turning once halfway, until tender and caramelized at the edges.
Brown the butter: while the carrots roast, melt the butter in a large skillet over medium heat. Cook, swirling the pan often, for 3 to 4 minutes, until the butter foams, then turns golden brown and smells nutty, with brown specks at the bottom. Remove from the heat immediately so it does not burn.
Make the glaze: stir the honey, garlic, thyme, and remaining 1/2 teaspoon salt into the brown butter. Return the skillet to low heat and cook for 30 seconds, just until the garlic is fragrant.
Glaze the carrots: add the roasted carrots to the skillet and toss gently until every carrot is coated in the glossy brown butter honey glaze. Stir in the lemon juice.
Serve: transfer to a serving platter, spoon over any extra glaze from the pan, and sprinkle with toasted pecans, extra thyme, and flaky sea salt, if using. Serve warm.