MELT 1 tbsp butter in a large frying pan over medium-high. Add bread cubes. Toast, stirring often for 3 to 4 min. Transfer to a plate.
RETURN pan to heat over medium-high. Add mushrooms. Cook, stirring often, until mushrooms are golden brown, about 12 min. Add remaining 2 tbsp butter, garlic, sage and 1/8 tsp salt. Reserve 1 1/2 cups mushrooms for polenta with mushrooms and fried egg.
WHISK oil with lemon zest, juice, Dijon and 1/8 tsp salt in a large bowl. Core and thinly slice fennel. Reserve fronds. Toss fennel, arugula and croutons with dressing. Divide salad among 4 plates. Top with mushrooms, goat cheese and walnuts.