Bring a large pot of well-salted water to a rolling boil. Add the carrots and blanch until tender, about 5 minutes. Remove the carrots from the boiling water and chill in an ice bath.
Meanwhile, heat up 1 tablespoon olive oil in a small sauté pan over medium-high heat. Add the shallots, sweat for 1 minute, then add the garlic and sweat for 1 more minute. Remove from the heat.
Place the carrots in a Vita-Prep blender or regular blender with the vinegar, orange zest and juice, turmeric and ginger and process at high speed. With the motor running, drizzle in about 1/2 cup of cold water to achieve a nice velvety consistency. Reduce the speed to its lowest setting and drizzle in 1/2 cup olive oil until it’s fully incorporated. Adjust the seasoning with salt and pepper; if you like it to be more acidic, you can add more orange juice or vinegar.
Divide the soup among four chilled bowls. Top each with a dollop of yogurt, a sprinkling of tarragon, a drizzle of olive oil and a little freshly ground pepper.