Heat olive oil in a stockpot over low heat until it begins to shimmer; add garlic. Cook, stirring occasionally, until fragrant, about 1 minute. Add sorrel and cook, stirring occasionally, until leaves are wilted and turn from bright green to a dull, khaki color, 3 to 4 minutes.
Place potatoes, vegetable stock, salt, thyme, and pepper into the pot. Bring mixture to a boil, about 5 minutes. Reduce heat, cover, and simmer until potatoes are tender, about 20 minutes. Remove from heat; let cool 10 minutes.
Pour in half-and-half. Blend mixture with an immersion blender until smooth. Taste and adjust salt if desired.
