One of my least favorite restaurant miso soup variations is when they just throw a few raw mushrooms slices into the bowl before serving. Raw button mushrooms have no flavor at all, and a rather unpleasant spongy texture. Grilling them beforehand, on the other hand, reduces their moisture content, concentrates the flavor so you can actually taste it, and adds that nice grilled-roasted flavor. Eggplants (aubergines) are also a lot tastier after grilling.
In Japanese cooking, grilling is usually performed without the addition of oil as a lubricant, so the pure flavor of the ingredient is preserved. I've grilled slices of eggplant and mushroom on a preheated cast iron grill pan  (which is much better for grilling on a ceramic-top or electric range than a traditional Japanese mesh grill) until brown on the outside before putting them into the dashi stock to finish cooking. As always, the miso is added at the end.
I've used the small, slim Asian style eggplant for this, not the big fat Mediterranean kind. If that is the only kind you can find, slice it rather thinly before grilling, and cut into quarters before adding to the soup. I used regular white mushrooms but you can use any mushrooms that you like.
I also added a little chopped up ginger shoot as a garnish. You can find green ginger shoots at a Thai or general Asian grocery store - or you may find that your ginger root has sprouted a shoot on its own. Finely julienned ginger root can be used instead if you dont' have any shoots.
The Official Taste Tester gives this one the best marks of the miso soups so far this week, pronouncing it "earthy and tasty".
Prepare the dashi stock following the instructions for Day 1 . Keep warm.
Preheat your grill pan until it's very hot.
Slice the eggplant into round slices. Slice the mushrooms to about the same thickness as the eggplant.
Line the grill pan with the mushrooms. (There's no need to oil the pan, the mushrooms will not stick.) Grill on both sides until they are marked with grill lines and have shrunken a bit. Toss them into the dashi soup stock and simmer.
Grill the eggplant slices in the same way, and put into the dashi soup. Continue simmering until the eggplant is tender, about 10 minutes. (You add the mushrooms first because they take longer than the eggplant to cook.
Chop the green part o the ginger shoots very finely.
Add the miso to the soup . Serve immediately, garnished with the chopped ginger shoots.