The sauce here is rather like a vegetarian version of the Piedmontese anchovy sauce, bagna cauda (though it’s even more umami-packed). It’s not one of those vegetable recipes that feels like a side dish, where you keep searching for the focus, but has enough different flavors and textures from each vegetable to be layered and surprising.
Trim the carrots at the top and tips (if there are long straggly bits on the tips). Leave the green tufts if there are any, but wash them really well. If you haven’t been able to get slim carrots, then halve them along their length.
Peel the celery root and cut it into wedges about ¾in thick. Put all the vegetables—except the Belgian endive—into a couple of roasting pans, or sheet pans that have a lip all the way around, in which they can lie in a single layer. Add the olive oil, season (don’t use too much salt, as the sauce will be salty), and toss everything around with your hands. Roast for 40 minutes, until tender and slightly scorched, turning them once. Quarter the Belgian endive heads and add halfway through, tossing them in the oil.
Make the sauce. Pound the walnuts in a mortar—or pulse-blend in a food processor—until you have a mixture that is part finely ground and part chunky.
Pour the olive oil into a saucepan set over a very gentle heat. Add the miso and whisk it together: the miso will stay in little globules separate from the oil, but that’s normal. Add the chili and garlic and simmer very gently for about 5 minutes, stirring every so often. The garlic must not color. Stir in the walnuts and cook for another 2 minutes.
Transfer the vegetables to a warmed platter. Either spoon the sauce over the top, or serve it on the side.