Heat 2 tbsp olive oil in large nonstick skillet over medium heat. Add potato, just 1 tsp mustard seeds, just 1 tsp garam masala, just 1 tsp cumin, ½ tsp salt, and a pinch of pepper and cook, stirring occasionally, until potatoes start to brown, 8 to 10 minutes. Add chickpeas and 2 tbsp water, cover, and cook until potatoes are tender and chickpeas are warmed through, 5 to 6 minutes. Lightly mash potatoes and chickpea filling with back of fork and transfer to medium bowl. Stir in cilantro and set aside. Wipe skillet clean.

Place tortillas, one at a time, in same skillet over medium-high heat and cook until warm and pliable, 1 to 2 minutes per side. Lay warmed tortillas on clean work surface. Divide samosa filling between wraps and top with tomato chutney. Carefully roll wraps, tucking in sides as you go. Cut wraps on a bias and transfer to serving plates.