Preheat the oven to 450 degrees F. Grease a rimmed baking sheet with 1 tablespoon of the olive oil.
Add the potatoes to a medium saucepan, cover them with cold water and add 1 tablespoon of salt. Bring the water to a boil, then simmer until the potatoes are tender when pierced with a knife or fork, 15 to 20 minutes. Drain the potatoes and spread onto the prepared baking sheet.
Using a heavy metal spatula or the bottom of a heavy glass, press each potato until it smashes. Drizzle with the remaining 1 tablespoon oil. Sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper. Bake until browned on top and bottom, 15 to 20 minutes.
While the potatoes are baking, add the pecans to a small skillet over medium heat and cook until toasted, 1 to 2 minutes. Add the butter and once melted, add the garlic and sprinkle with 1/2 teaspoon each salt and pepper. Cook until the garlic softens and starts to brown, 2 to 3 minutes, then stir in the thyme. Remove from the heat.
Transfer the potatoes to a serving dish. Pour the garlic pecans over and toss lightly until coated. Sprinkle more fresh thyme on top. Serve immediately.