Sweet potatoes make the perfect gluten-free crust for this custardy quiche. Brown the mushrooms with garlic to deepen their meaty flavor.
Preheat oven to 400°F. Spray a 9-inch pie plate with cooking spray; line with sweet potato in overlapping circles. Bake at 400°F until tender, about 15 minutes. Remove from oven; press sweet potato into dish. Reduce oven temperature to 375°F.
Heat olive oil in a large skillet over medium-high; swirl to coat. Add mushrooms; cook, stirring occasionally, 5 minutes. Add garlic, and cook until mushrooms are browned and tender, 2 to 3 minutes. Remove from heat; set aside.
Whisk together eggs, milk, cheese, Swiss chard, salt, and pepper in a medium bowl. Place mushrooms in an even layer in sweet potato crust. Pour egg mixture over mushrooms. Dollop with pesto; swirl into egg mixture with a knife. Bake at 375°F until set in center, about 20 minutes. Let cool slightly. Cut into 8 slices.