How to Make It
Place potatoes and water in a medium-size microwavable bowl; cover tightly with plastic wrap. Microwave on HIGH until fork-tender, about 4 minutes. Spread potatoes in a single layer on a baking sheet lined with paper towels; let dry 5 minutes.
Heat oil in a Dutch oven over medium-high. Add potatoes and garlic; cook, stirring occasionally, until golden brown and crispy, 6 to 8 minutes. Transfer potatoes and garlic using tongs to a plate lined with paper towels; discard garlic. Sprinkle potatoes with ½ teaspoon of the salt. Set aside.
Add shallot and butter to Dutch oven over medium-high. Cook, stirring often, until softened, about 1 minute. Stir in cider, mustard, tarragon, and remaining ½ teaspoon salt; bring to a simmer. Add mussels; cover and simmer until mussels open, 3 to 4 minutes. Remove and discard any mussels that do not open.
Transfer mussels to 4 shallow serving bowls using a slotted spoon. Cook broth mixture over medium-high, uncovered, until reduced slightly, about 2 minutes. Remove from heat; let stand 5 minutes. Place cream in a small bowl; slowly whisk in broth. Spoon mixture over mussels. Add potatoes to mussels; sprinkle with parsley leaves. Serve immediately.