Place the porcini mushrooms in a bowl and cover with boiling water. Let sit until softened, 30 minutes.
Heat the grill to high.
Brush the cremini or white button mushroom caps with the canola oil and season with salt and pepper. Place the mushrooms on the grill, cap side down and grill until golden brown and slightly charred, 4 to 5 minutes. Turn the caps over and continue grilling until the mushrooms are cooked through, about 5 minutes longer. Remove from the grill, let cool slightly then coarsely chop.
Remove the porcinis from the soaking liquid and place in the bowl of a food processor with a few tablespoons of the soaking liquid. Add cremini mushrooms, garlic pulp, walnuts, parsley and thyme in a food processor and process until finely chopped. With the motor running, slowly add 1/2 cup of the olive oil and process until smooth. Add 1/4 cup of the Romano cheese and pulse a few times to incorporate. Season with salt and pepper.
Brush the bread on the cut side with the remaining 1/4 cup of olive oil and season with salt and pepper. Evenly spread the pesto over the cut side of each half of bread. Top the pesto with the fontina cheese, return to the grill, cheese side up, close the cover of the grill and cook until the cheese has melted, about 2 minutes. Remove from the grill and sprinkle with the remaining Romano.