Finely chop lemongrass, ginger, and garlic in a food processor.

Heat vegetable oil in a large pot over medium heat.

Add the lemongrass mixture to the pot and cook until golden brown, seasoning with salt.

Incorporate red curry paste and tomato paste, cooking until darkened.

Stir in crushed tomatoes, scraping up any browned bits and cooking until thickened.

Add coconut milk and season with salt. Bring to a boil, then reduce heat and simmer until rich.

Add sweet potatoes and carrots, then cover with water.

Partially cover the pot and cook until carrots are crisp-tender.

Add shallots and cook until sweet potatoes are tender and shallots are soft.

Stir in the sliced red Thai chile (if using) and lime juice.

Spoon the curry over steamed jasmine rice.

Garnish with thinly sliced scallions, basil leaves, and cilantro leaves. Serve with lime wedges.