Place the Kashmiri peppers (seeds removed) in a bowl of water for 30 minutes to rehydrate them. Remove them from the water and using a mortar and pestle, crush the chilies into a paste.
In a sauce pan over medium heat, heat 1/2 of the sesame oil, then sauté the ginger and garlic until fragrant (30 seconds to 1 minute).
Lower the heat to low and add the Kashmiri paste. Simmer the chilies, ginger, and garlic for 1 minute, stirring often.
Add the remaining sesame oil and the tomatoes. Continue to simmer, stirring often, for 1 to 2 minutes.
Add the black pepper, salt, soy sauce, and spring onion leaves. Turn the heat up to medium and continue to cook, stirring often, until integrated and the sauce slightly thickens.
Add the lemon juice, stirring often, for one additional minute, then remove the sauce from the heat.
Allow the sauce to cool to room temperature - the sauce will thicken more in the process. Use immediately or store in the refrigerator in an airtight container for up to 2 weeks.
Want to add extra fire to your sauce? Try mixing in a few Tien Tsin peppers among the Kashmiri. Their Scoville heat rating is 50,000 - 75,000 SHU - a world's difference from the 1,000 - 2,000 SHU of Kashmiri. Be careful - the sauce can become extremely hot. Use two to three substituted in with your first making, and adjust upward or downward from there to get the heat level best for you.