Preheat oven to 375°F.
Melt the butter in a medium saucepan over medium-high heat. Add the buckwheat, and stir to coat. Cook 2-3 minutes, until the groats smell slightly toasty. Pour in the broth (or water), and bring to a boil. Lower heat to low, cover, and simmer for 10 minutes, until all the liquid is absorbed. Remove from heat and let sit, covered, for 5 minutes.
When buckwheat is ready, add the groats, lentils, root veggies, garlic, tomato paste, tamari, Worcestershire sauce and a pinch of salt to a food processor. Pulse 5-7 times, just until coarsely chopped and forming together. Turn out onto a baking sheet lined with parchment paper, and shape into a roughly 4×8-inch loaf.
Stir together ketchup, dried mustard and vinegar in a small bowl. Brush the loaf with the ketchup glaze. (You’ll have a good amount leftover for more glazing.)
Bake loaf for 30 minutes, brush again with glaze, and bake for another 10-15 minutes, until a toothpick inserted into the center comes out clean.
Brush loaf with remaining glaze, and let the loaf rest for 5 minutes before slicing.