Heat 1/3 cup of the vegetable oil in a 10-inch nonstick ovenproof saute pan over medium-high heat until it shimmers. Carefully add the jalapeno and scallions. Turn off the heat and stir to combine. Cook in the hot oil for 1 minute, stirring constantly. Stir in the sesame oil and season lightly with salt. Remove to a bowl and set aside until ready to serve. Wipe the pan clean.
Heat the broiler with a rack set in the middle of the oven.
Pulse the ham, onions and mustard in the bowl of a food processor until a chunky paste forms.
Whisk the eggs and heavy cream in a mixing bowl.
Heat the remaining vegetable oil in the same saute pan over medium-high heat. Add the pureed ham mixture and saute until the onions have softened and the mixture is lightly browned in parts, about 5 minutes, stirring occasionally. Reduce the heat to medium and wait 2 minutes in order for the pan to come down to temperature; continue stirring. Pour the beaten eggs over the ham, mix together and cook until the eggs start to set, about 2 minutes. Sprinkle with the cheese and continue to cook until the frittata is almost set but the top is still runny, 5 to 7 minutes.
Place the frittata under the broiler and broil until the top is golden brown, 3 to 5 minutes. Let stand for 5 minutes. Using a rubber spatula, loosen the frittata from the pan and invert onto a plate. Cut into wedges and serve topped with the jalapeno and scallion relish. Serve alongside a lightly dressed green salad if desired.