Step 1

Cook oil, mustard seeds, and turmeric in a large skillet over medium-high, stirring occasionally, until seeds begin to pop, about 1 minute. Add onions and season with salt. Cook, stirring occasionally, until onions are beginning to soften, about 4 minutes. Reduce heat to medium-low and cook, stirring occasionally, until onions are softened and jammy and starting to brown around the edges, 15–20 minutes. Set jam aside.Do ahead: Jam can be made 1 week ahead. Transfer to an airtight container; cover and chill.

Step 2

Purée scallions, chile, garlic, ginger, cilantro, mint, lemon juice, a big pinch of salt, and ⅔ cup water in a blender until smooth. Transfer to a small bowl. (Makes about 2 cups. Store leftovers in an airtight container; cover, chill, and use within 3 days.)

Step 3

Place potatoes in a large pot and pour in cold water to cover by 1". Add a large handful of salt (water should taste briny) and bring to a boil. Reduce heat; simmer until potatoes are very tender but not falling apart, 30–35 minutes. Drain and let sit until cool enough to handle. Peel potatoes and slice ¼" thick. Let cool completely.

Step 4

Slather one side of bread slices with scallion chutney. Distribute half of Monterey Jack and half of cheddar over 8 slices. Top with some reserved onion jam, followed by 3–4 potato slices. Sprinkle with chaat masala, then top with remaining cheese; close up sandwiches.

Step 5

Heat 1 Tbsp. ghee in a large nonstick skillet. Place 1 or 2 sandwiches (as many as will comfortably fit) in skillet, lay a baking sheet or skillet on top, and cook, pressing, until bottom sides of sandwiches are golden brown, about 4 minutes. Turn sandwiches over and add a bit more ghee to pan if needed. Cover again and cook, pressing, until other side is golden brown and cheese is melted, about 4 minutes. Transfer to a cutting board and cut into quarters. Repeat with remaining ghee and sandwiches.