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Remove the core from each tomato. Roughly chop the tomatoes and put into a blender with about 1 teaspoon of salt. Pulse the tomatoes until almost pureed but with a few chunks remaining. Pour the blended tomatoes into the cheesecloth-lined strainer and refrigerate. The tomato mixture will slowly drip clarified tomato water into the bowl. This will take 2 to 3 hours to completely drip out of the puree and can be done overnight.
Pour the tomato water into a medium pot. (The remaining puree can be saved for another recipe or discarded.) Bring the tomato water to a boil over medium heat. Reduce the heat, add the ginger, garlic and lemongrass to the liquid and simmer for 3 minutes. Foam will start to form at the top of the tomato water and should be skimmed off. Season with salt and pepper.
Place the rice noodle pieces in a medium pot. Pour the tomato consomme through a strainer over the pot with the noodles in it, removing the aromatics. Bring the consomme back to a simmer and fully cook the noodles.
With a slotted spoon, scoop equal amounts of the noodles into 4 serving bowls. Pour the consomme over the noodles in the bowls. Garnish the top with the scallions, sliced cherry tomatoes, a few drops of extra-virgin olive oil and 2 or 3 slices of the hot peppers. Serve immediately.