Heat a large saucepan over medium-high heat. Add canola oil to pan; swirl to coat. Add shallots; sauté 2 minutes. Add curry paste and garlic; sauté 1 minute. Add stock and coconut milk; bring to a boil. Reduce heat; simmer 20 minutes.
Combine chicken, cucumber, basil, sambal oelek, and sesame oil in a medium bowl; toss to coat. Place 1/2 cup chicken mixture and 1/2 cup noodles in each of 4 bowls. Pour about 1 1/4 cups stock mixture into each bowl. Serve with lime.
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