Heat the oven to 425°F and lightly grease a 9-inch round griddle, skillet, or baking sheet.
To make the crust, whisk together the flour, baking powder, and salt. Cut the cold butter into cubes and then add to the flour. Working quickly with your hands or a pastry cutter, work the butter into the dough until the dough is crumbly. Pour in the half and half and stir until everything has come together and a shaggy dough is formed.
Pat the dough out evenly into the griddle or skillet. (If using a skillet, don’t work the dough up the sides—leave it just on the bottom). If using a baking sheet, pat out a 9-inch circle. Poke the dough with a fork about 4 or 5 times, and place the dough into the oven. Cook it uncovered for 5 minutes then remove from the oven.
Meanwhile, heat a large skillet to medium-low heat. Add the chorizo and while occasionally stirring, cook for 5 minutes or until it changes from a bright red to a more brownish red. Leaving on the skillet, remove the chorizo with a slotted spoon and place it in a bowl. (It’s okay if there is some chorizo grease in the skillet, as this adds flavor. If there is an excess of grease, however, feel free to drain and discard it.)
Add to the skillet the butter. Whisk together the eggs, half and half, salt, and pepper. When the butter has melted, pour in the eggs. Let them sit for 1 minute then add the chorizo back into the skillet and gently stir until they are loosely set. Taste the eggs with the chorizo and add a pinch of salt if you think it needs it, though I find that usually the chorizo adds enough flavor and salt isn’t necessary.
Turn off the heat and then spoon the eggs out of the skillet and spread evenly onto the partially baked pizza crust. (You did remember to remove it from the oven, didn’t you!)
Top the eggs evenly with the cheese, then top the cheese evenly with the onions and jalapeños. Return the pizza to the oven and cook uncovered for 8 to 10 more minutes or until the cheese is melted and the crust is lightly browned.
Remove the pizza from the oven and sprinkle fresh cilantro leaves over the baked pizza. If you like, serve each slice topped with pico de gallo, avocado slices, and/or crumbled Cotija cheese.