Bring a large pot of salted water to a boil. Add the rinsed baby yellow potatoes and cook until fork-tender, about 15 minutes. Drain and let cool slightly.
Preheat the oven to 400°F (207°C). Line a baking sheet with parchment paper.
Arrange the cooked potatoes on the prepared baking sheet. Using the bottom of a small saucepan or a flat heavy object, gently press each potato to flatten it to about 1/2-inch thick.
Brush the smashed potatoes with the olive oil, then season with salt and ground black pepper.
Bake until the potatoes are golden brown and crisp around the edges, about 15–20 minutes.
Brush each baked potato generously with garlic pesto, then sprinkle with chopped parsley. Serve immediately.