Peel the swede and chop it into chunks around 2-3cm across. Trim and peel the carrots, then thickly slice them.
Warm 2 tbsp oil in a large pan, then add the swede and carrots and season with a small pinch of salt and pepper. Fry, stirring every so often, for 5-8 mins till the veg are lightly browned and softened. While the veg fry, fill your kettle and boil it.
Add half the thyme sprigs to the pan (keep the rest for later). Carefully pour 1 ltr boiling water into the pan – it will splutter when you add the water so just add a little to start, then pour in the rest once the pan has calmed down. Cover the pan with a lid, turn up the heat and bring to the boil. Once it’s boiling, turn the heat down and simmer for 15-20 mins, till the veg are tender
While the veg simmer, pick the leaves off the remaining thyme sprigs – you can push the woody sprigs through a fine mesh sieve. The sprigs will pass through the mesh and the leaves will collect in the sieve.
When the veg are tender, drain them then tip them back into the pan. Pick out the thyme sprigs and discard them.
Pop the pan back on a low heat and warm for 1-2 mins, stirring often, to sizzle off any excess water. Pour in 150ml of the milk (keep the rest for your Yorkies) and 50g of the butter (keep the rest for your other recipes). Keep the pan on the heat and warm the milk through 2-3 mins, stirring often. Take the pan off the heat and use a potato masher to gently mash the carrots and swede together.
When the mash is smooth, add the remaining thyme leaves. Stir to mix, taste and add more salt or pepper if you think the mash needs it. Spoon the mash into a warm bowl and serve.