Place the whole potatoes in a pot of cold salted water so that they are covered. Bring to a boil over high heat, then reduce heat to medium-low and simmer until the potatoes are just tender when pierced, 18 to 20 minutes.
Drain the potatoes and dump them on a baking sheet. Let cool for 5 to 10 minutes.
When the potatoes are cool enough to handle, use the heel of your hand or the bottom of a small glass and firmly press on the potato until it begins to break. You don't need to completely flatten the potatoes; just press them until they begin to break apart.
Drizzle the potatoes with oil and season with salt and pepper. Gently toss them to coat. It's ok if some of the potatoes fall apart.
Heat your griddle to medium-low. Arrange the potatoes in a single layer and cook, with the griddle covered if possible, flipping occasionally, until golden brown and crispy, about 30 minutes total.
While the potatoes are cooking, mix the melted butter and herbs in a small bowl. During the last 5 minutes of cooking, brush generously with the herb butter.
Transfer the potatoes to a platter and serve immediately.
Notes
Don't let them cool completely--After boiling the potatoes, let them cool slightly but don't let them cool completely. They'll be easiest to smash when they're still a little warm.
Adjust the temperature--If your potatoes are crisping up too quickly or getting too dark, reduce the heat. I find that for a covered Blackstone griddle, medium-low heat works best. If you're using an uncovered griddle, the temperature may need to be closer to medium.
Storage and reheating--Store leftover smashed potatoes in a sealed container in the fridge or your cooler for up to 3 days. Reheat over low heat on the griddle, or in a warm oven.
Dietary--This recipe is suitable for gluten-free and vegetarian diets. To make it vegan or dairy-free, use oil instead of butter.