In a 9 1/2- or 10-inch non-stick skillet, brown the sausage over medium heat, breaking it up into smaller pieces as it cooks. Add the potatoes and thyme, increase heat to medium high and cook, turning occasionally with a spatula, until the potatoes partially brown – 12-15 minutes.
Meanwhile, beat eggs and salt in a large bowl. Add pecans, Parmesan, and red pepper. Stir potato mixture into egg mixture and stir until well combined.
Lightly coat skillet with vegetable oil cooking spray and place over medium heat. Add potato mixture, pressing it firmly into skillet in an even layer, using the back of a spatula. Cook 8 minutes. Invert skillet onto a cookie sheet to release tortilla bottom-side-up; it should be well browned. Spray skillet again and slide tortilla back into skillet to brown other side – about 8 minutes longer. To serve, slide tortilla onto serving plate. Cool at least 10 minutes before slicing.
Nutrition information per serving: calories: 738; protein: 21g; carbohydrate: 62g; saturated fat: 16g; monounsaturated fat: 22g; polyunsaturated fat: 6g; cholesterol: 109 mg; fiber: 5g; sodium: 824mg.