Heat a medium saucepan over medium-high heat. Add oil and garlic, cook until sizzling and fragrant, about 1 minute. Stir in potato and 1/2 teaspoon salt. Cook 1 minute.
Add stock and 1 1/2 cups of water and bring to a boil. Reduce to a simmer and cook for 5 minutes. Stir in watercress. Return to a boil. Reduce to a simmer for 1 minute. Season with salt and pepper. Divide among soup bowls and squeeze a lemon wedge into each bowl. Serve immediately.