Prepare the ingredients: peel and smash 2 garlic cloves into a chunky paste using the flat side of a knife; thinly slice and grate ½ teaspoon ginger; finely slice 1 shallot; thinly slice 1 medium carrot; remove stems from 3 mushrooms and thinly slice them; slice the bok choy into 1‑inch‑thick pieces; measure 4 cups sodium-free chicken stock, 1 teaspoon red curry paste, ½ teaspoon sugar, 7 ounces Pad Thai noodles, 1 pound shrimps (peeled and deveined), juice of ½ lemon, and a handful of chopped scallions.
In a large heavy-bottom pan, combine 4 cups sodium-free chicken stock, the sliced shallot, the prepared ½ teaspoon ginger, ½ teaspoon sugar, and the sliced carrot. Bring the mixture to a simmer over medium heat.
Add the smashed garlic paste to the simmering stock and stir once to combine; let simmer about 30 seconds.
Stir in 1 teaspoon red curry paste and add the sliced mushrooms. Simmer for 1–2 minutes to meld flavors.
Add 7 ounces Pad Thai noodles to the pan, push them gently into the liquid so they are submerged, and cook for 3 minutes, stirring occasionally to separate the noodles.
Add 1 pound shrimps (peeled and deveined) and the sliced bok choy to the pan. Cook until the noodles are tender and the shrimp are opaque and cooked through, about 2–4 minutes.
Remove the pan from the heat and squeeze the juice of ½ lemon into the soup.
Divide the soup among bowls and garnish each serving with a handful of chopped scallions. Serve immediately.