Drop the potatoes into a large pot of boiling salted water and cook for 20 to 30 minutes, until they are just cooked through. Strain the potatoes and set aside, leaving the water boiling in the pot.
Drop the green beans into the boiling water. Boil until just cooked and bright green, 3-5 minutes, being careful not to overcook. Drain and rinse with very cold water to stop the cooking process.
Make the dressing by combining the garlic, honey, mustard, salt, and red wine vinegar in a small bowl, whisking to combine. Stream in the olive oil, whisking until well incorporated.
When the potatoes are cool enough to handle slice in half. Add the sliced potatoes, green beans, and shallots to a large bowl. Pour over the dressing and stir to combine. Let sit at least 10 minutes for the dressing to absorb. Sprinkle with parsley, then serve immediately or cover and refrigerate for up to 2 days. Best served at room temperature.