Preheat the oven to 350 degrees F. Position the rack in the upper third position.
Heat 1 tablespoon olive oil in a 3- to 4-quart braiser over medium-high heat. Add the ham and cook until golden brown, 4 to 5 minutes.
Add the remaining tablespoon olive oil, along with the onions and leeks. Season with salt and pepper. Cook until translucent and fragrant, 4 to 5 minutes. (You want the veggies to be cooked three-quarters of the way, because they will continue to cook in the oven.)
Add the asparagus and garlic and saute until just tender, around 4 minutes. (There shouldn't be too much color on the vegetables.)
Add the peas. Stir to combine, then remove from the heat. Allow to cool slightly while you make the custard filling.
In a large mixing bowl, whisk together the eggs, cream, Dijon mustard, 1/2 teaspoon salt and a couple turns of black pepper. Pour over the veggie and ham mixture. (The vegetables should be visible and not swimming in the eggy mixture. That way the potato tots don't sink!)
Top the vegetables and eggy mixture with dollops of cream cheese. Sprinkle the Cheddar in an even layer over the dollops of cream cheese.
Arrange the potato tots in a uniform pattern on top of the custard filling. Sprinkle the potato tots with salt and pepper. (If you have remaining tots, bake them off and snack on them later!)
Bake in the top third of the oven until the potato tots are golden brown and the eggy mixture is set, about 40 minutes. (You can stick a fork in the mixture to ensure that it is cooked through.)
Sprinkle with the fresh dill, chives and a few splashes of hot sauce to serve and enjoy!
Store in airtight container or wrapped tightly with plastic wrap for no more than 3 days in the fridge after being cooked. Do not freeze.
You can cook and prepare each component of the dish ahead of time and assemble when ready to bake!