While preheating oven to 400°F/200°C/Gas Mark 6, toss yams with olive oil, salt and pepper. Spread in 1 layer on a baking sheet.
Bake the yams until tender (20 minutes). Remove from oven. Chill until cooled to room temperature.
While chilling the yams, add 1 tbsp olive oil into a skillet, heat over medium heat. Caramelize the garlic and onion in oil for 15 minutes or till they become golden brown. Stir in kale, let wilt. Spoon the mixture into a bowl, refrigerate until cooled to room temperature.
In a large bowl, combine the cooled ingredients, add thyme and vinegar, season with salt and pepper. Stir gently and serve.