1. To prepare dressing, combine first 7 ingredients in a mini food processor; process until smooth.
2. To prepare salad, cook bacon in a nonstick skillet over medium heat until crisp. Remove bacon from pan; crumble. Add canola oil to pan; swirl to coat. Add chicken to pan; sauté 6 minutes on each side or until done. Cool slightly; shred with 2 forks.
3. Pierce 10 holes on one side of the bottom of a 13 x 9-inch disposable aluminum foil pan. Place holes over element on cooktop; place wood chips over holes inside pan. Place a shallow ovenproof bowl on opposite end of pan. Add chicken and stock to bowl. Heat element under holes to medium-high; let stand 1 minute or until chips begin to smoke. Carefully cover pan with foil. Reduce heat to low; smoke chicken 10 minutes. Remove from heat. Drain.
4. Combine spinach, romaine, and basil in a large bowl; toss. Arrange 2 cups spinach mixture on each of 4 plates. Divide bacon, chicken, 1/3 cup avocado, tomatoes, eggs, and cheese evenly among plates. Drizzle about 3 tablespoons dressing over each salad.