Preheat oven to 500°F. Combine 4 tablespoons oil and thyme in large bowl. Press 2 garlic cloves into oil with garlic press; whisk to blend. Add chanterelles and toss to coat. Sprinkle with salt and pepper.
Spray rimmed baking sheet with nonstick spray. Spread mushroom mixture on sheet. Roast mushrooms until tender, stirring occasionally, about 6 minutes.
Cut Speck crosswise into 1/4-inch-thick strips. Heat 1 tablespoon oil in small skillet over medium-high heat. Add Speck; sauté until crisp, 4 minutes. Drain on paper towels.
Toast ciabatta slices until golden; rub with remaining garlic clove. Drizzle with 1 tablespoon oil. Halve each slice lengthwise.
Fill large skillet with water and bring to boil. Add 1/2 teaspoon salt. Crack eggs, 1 at a time, into custard cup, then slide egg from cup into water; reduce heat to low. Poach eggs until whites are set and yolks are softly set, 3 to 4 minutes.
Meanwhile, toss lettuce and mâche with enough vinaigrette to coat. Mound salad on 6 plates. Using slotted spoon, remove eggs from water, dab with paper towels to absorb excess liquid, and place atop salads. Garnish with mushrooms and Speck. Place ciabatta fingers around salad and serve immediately.