Halve and core pears; shred one pear half. In a medium bowl combine shredded pear, thyme, salt, and pepper. Add ground turkey; mix well. Shape into four 3/4-inch-thick patties.
Grease grill rack. Grill remaining pear halves, covered, over medium heat 6 to 8 minutes or until tender and lightly charred, turning once. Remove from grill. Grill patties, covered, 12 minutes or until no longer pink (165 degrees F), turning once.
Thinly slice grilled pears. For slaw, in a large bowl combine sliced pears and next five ingredients (through pecans). In a small bowl combine remaining ingredients. Pour mayonnaise mixture over cabbage mixture; toss to coat. Season to taste with additional salt and pepper. Serve burgers with slaw.
In a wide-mouth pint jar or 2-cup liquid measuring cup combine first five ingredients (through cayenne pepper). Slowly add oil. If necessary, let stand until oil separates from egg mixture.
Using an immersion blender, hold blender against bottom of jar and blend 20 to 30 seconds. When mixture is nearly combined and thickened, move blender up and down while blending to incorporate any remaining oil. (Or in a medium bowl whisk together first five ingredients [through cayenne pepper]. Slowly add oil in a thin, steady stream, whisking constantly until combined and thickened.)
Cover jar or transfer mayonnaise to an airtight container. Store in the refrigerator 3 to 5 days.