Soft cook the **eggs**. (Bring ½” water to boil, add eggs, turn down to medium, cover, cook for 6½ minutes. Immediately remove and cool in ice bath.)
While the **eggs** cook, in a large pan (nonstick, if you have one), heat 2 teaspoons of olive oil on medium-high until hot. Add the **mushrooms**; cook, stirring occasionally, 3 to 4 minutes, or until lightly browned. Add the **yu choy**; season with salt and pepper. Cook, stirring occasionally, 2 to 3 minutes, or until wilted. Add the **endive**; season with salt and pepper. Cook, stirring occasionally, 1 to 2 minutes, or until softened. Transfer to a bowl; season with salt and pepper to taste.
In the same pan, heat 1 teaspoon of olive oil on medium-high until hot. Add the **ginger**, **seasoned plum**, and as much of the **jalapeño** as you’d like, depending on how spicy you’d like the dish to be; season with salt and pepper. Cook, stirring occasionally, 1 to 2 minutes, or until softened. Add **¾ cup of water**; season with salt and pepper. Cook, stirring occasionally and gently smashing the plum with a spoon, 8 to 9 minutes, or until the plum has broken down. Add the **black bean sauce** and **2 tablespoons of water**. Cook, stirring frequently, 1 to 2 minutes, or until combined. Turn off the heat. Season with salt and pepper to taste.
Once the sauce has cooked for about 10 minutes, add the **rice cakes** to the pot of boiling water. Cook 2 to 3 minutes, or until tender. Reserving **½ cup of the rice cake cooking water**, drain thoroughly. Transfer to the pan of **sauce**; add the **cooked vegetables**, **crème fraîche**, **butter**, **half the garlic chives**, and **half the reserved rice cake cooking water**. Cook on medium-high, stirring frequently, 1 to 2 minutes, or until coated and thoroughly combined. (If the sauce seems dry, gradually add the remaining rice cake cooking water to achieve your desired consistency.) Turn off the heat; season with salt and pepper to taste.
Transfer the **peeled eggs** to a cutting board and halve lengthwise; season with salt and pepper. Divide the **finished rice cakes** between 2 dishes. Top with the seasoned eggs. Garnish with the **peanuts** and **remaining garlic chives**.