Step 1

Purée chile, garlic, cilantro, mint, lemon juice, peanuts, salt, sugar, cumin seeds, and ¼ cup water in a blender, scraping down sides as needed, until very smooth. Set cilantro-mint chutney aside.Do Ahead: Chutney can be made 1 day ahead. Transfer to a jar; cover and chill.

Step 2

Pierce potatoes all over with a paring knife and place in a medium saucepan. Pour in cold water to cover by 1". Bring to a boil and cook until potatoes are fork-tender, 18–20 minutes. Drain and let cool slightly. Rub off skins with paper towels; discard. Cut potatoes into ¼" pieces.

Step 3

Meanwhile, heat 2 Tbsp. oil in a large skillet over medium-low. Add onion and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and cook, stirring occasionally, until onion is soft and deeply browned, 10–12 minutes. Transfer to a bowl; reserve skillet.

Step 4

Coarsely grind coriander seeds and fennel seeds in spice mill or mortar and pestle.

Step 5

Heat remaining 2 Tbsp. oil in reserved skillet over medium. Add green chile, ginger, cumin seeds, and ground fennel and coriander. Cook, stirring, until fragrant, about 1 minute. Stir in potatoes and peas until well combined; cook 1 minute. Stir in amchur powder, garam masala, chile powder, and remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and cook, stirring occasionally, 2 minutes. Stir in cilantro, lemon juice, and sugar and cook, still stirring, another 2 minutes. Remove from heat.

Step 6

Unfold puff pastry on a lightly floured surface and roll out to a 9½"–10" square. Transfer to a parchment-lined rimmed baking sheet.

Step 7

Spread onion over pastry, leaving a 1" border. Scatter Fontina over onion and press lightly with a spatula. Top with potato mixture; press to flatten.

Step 8

Whisk together cream and sugar in a small bowl. Brush edges of tart with cream mixture. Freeze tart until pastry is firm, about 10 minutes.

Step 9

Place a rack in middle of oven; preheat to 400°. Bake tart until crust is golden brown, 35–40 minutes. Let cool 10–15 minutes, then cut into squares.

Step 10

To serve, scatter pomegranate seeds and cilantro over tart. Drizzle tamarind-date chutney and reserved cilantro-mint chutney on top and/or serve alongside.Do ahead: Tart can be assembled 1 day ahead. Wrap in plastic and freeze. Thaw 1 hour in fridge before baking.