Heat a Dutch oven over medium heat and brown the lamb chunks in batches until they develop color on all sides. Remove the lamb and set it aside.
Add the onion and carrots to the pot and cook until the onion softens. Stir in the tomato paste and cook for one minute.
Return the lamb to the pot along with the broth, thyme, salt, and pepper. Bring the mixture to a simmer, then cover and cook for 45 minutes.
Add the turnips, parsnips, and potatoes. Continue simmering uncovered for 30 to 40 minutes until the vegetables are tender and the lamb is soft.
While the stew simmers, heat the oven to 425°F. In a mixing bowl, combine the flour, baking soda, and salt. Pour in the buttermilk and stir until a dough forms.
Turn the dough onto a lightly floured surface, shape it into a round loaf, and cut a cross on top. Place it on a baking sheet and bake for 30 minutes until the crust is golden.
Let the soda bread cool slightly before slicing. Serve warm pieces with bowls of the finished stew.