Heat the oven to 180°C fan / 200°C conventional / Gas 6.
Peel and trim the parsnips, then cut lengthways into evenly sized halves or quarters. Cut out any tough, woody cores from larger parsnips.
Toss with the oil, salt and pepper. Spread across a large roasting tin in a single layer, leaving a little space between the pieces.
Roast for 25–30 minutes, turning halfway through, until beginning to soften and turn golden.
Gently melt the butter in a small saucepan. Stir in the honey and mustard, if using.
Drizzle over the parsnips, add the thyme and turn gently to coat. Return to the oven for 15–20 minutes, until tender and caramelised. Check towards the end, as the honey can catch.
Serve in a warm dish, spooning over any buttery glaze from the tin.