Soak skewers in warm water. Clean the mushrooms using a damp paper towel and rinse the apple, pepper, and zucchini. Cut the mushrooms in half from top to bottom. Core and chop the apple into 1-inch pieces. Trim and deseed the pepper; chop into pieces the size of the apple and mushroom halves. Halve zucchini lengthwise, slicing into thick half moons.
Turn the broiler to high. Take a wooden skewer and alternate placing the apple, mushrooms, pepper, and zucchini for a total of 2 slices of each per skewer. Put the skewers on a baking sheet and drizzle with 1 tablespoon vegetable oil. Sprinkle with generous pinch of salt and a small pinch of pepper across skewers. Roast in oven until the apple begins to caramelize, about 6 to 8 minutes.
In a small bowl, mix the cornstarch and 1 tablespoon of water into a “slurry” and set aside. In a small saucepan, whisk 1/4 cup water, instant coffee, soy sauce, sugar, a pinch of black pepper, and the cornstarch slurry together. Bring to boil over medium-high heat, then reduce heat to low while whisking occasionally. Allow the mixture to thicken for about 2 to 3 minutes.
Rinse the orange and zest 1 tablespoon of it, adding it into a large bowl. Supreme the orange by trimming both ends and cutting away the peel and pith. Remove the flesh segments and squeeze the remaining juice into the bowl. Slowly whisk in 1 tablespoon of vegetable oil and season with salt and pepper. Rinse, destem, and thinly slice the kale, adding it to the bowl along with the edamame and toss.
Drizzle skewers with coffee teriyaki sauce while they are on the baking sheet and serve with the citrus edamame salad.