Make the Vinaigrette: Combine the olive oil, red wine vinegar, Dijon mustard, minced garlic, kosher salt, and black pepper in a small bowl. Whisk until smooth and set aside for later.
Cook the Potatoes: Fill a large pot with water and add a generous tablespoon of salt. Bring it to a boil, then lower the heat to a gentle simmer. Add the potatoes and cook until they are tender, about 20 minutes. Use a slotted spoon to transfer the cooked potatoes to a cutting board and let them cool.
Prepare the Eggs: While the potatoes are cooking, bring a medium pot of water to a boil. Reduce the heat slightly, gently place the eggs in the water, and cook them for 8 minutes to achieve a soft, jammy yolk. Transfer the eggs to an ice bath to cool for a few minutes. Once cooled, peel the eggs and cut them in half.
Blanch the Green Beans: Bring the medium pot of water back to a boil and add the trimmed green beans. Cook for 4–5 minutes, just until tender. Drain the green beans and immediately place them in the ice bath to stop the cooking process. Once cooled, pat them dry with a paper towel.
Assemble the Salad: Slice the cooled potatoes into halves or quarters, depending on their size. In a large bowl, combine the potatoes, green beans, and chopped herbs. Drizzle the vinaigrette over the mixture and toss gently to coat everything evenly. Arrange the egg halves on top and season with extra salt and pepper before serving, if desired.