Rinse baby potatoes thoroughly under cold water. Place them in a large pot and cover with cold water, adding 1 tablespoon of salt. Bring to a boil over high heat, then reduce to medium and simmer until fork-tender, about 20-25 minutes.
While the potatoes are cooking, preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper or lightly oil it to prevent sticking.
Drain the potatoes thoroughly and let them steam dry for 5 minutes. Transfer them to the prepared baking sheet, spacing them evenly. Using the bottom of a measuring cup or a potato masher, gently press down on each potato until it's flattened to about ½-inch thickness.
Drizzle the smashed potatoes with olive oil, making sure each gets a generous coating. Sprinkle with minced garlic, rosemary, salt, and pepper. Roast in the preheated oven for 20-25 minutes, or until the edges turn golden brown and crispy. For extra crispiness, broil for the final 2 minutes, but watch carefully to prevent burning.
While the potatoes roast, whisk together the Greek yogurt, lemon juice, Dijon mustard, dill, chives, and honey (if using) in a medium bowl. Season with salt and pepper to taste. The dressing should have a pourable consistency—if it's too thick, thin it with a splash of water or additional lemon juice.
Allow the crispy smashed potatoes to cool for 5-10 minutes before assembling. Transfer the potatoes to a serving dish, drizzle with the yogurt dressing, and scatter the green onions, parsley, capers, and lemon zest on top.