I peel and cube the potatoes, then drop them into a pot of salted, cold water before turning on the heat. This helps them cook evenly all the way through. Once they're fork-tender, about 15 minutes, I drain them and mash them with warm milk and butter until smooth.
While the potatoes cook, I whisk together the grainy mustard, honey, apple cider vinegar, and minced garlic in a small bowl. This glaze does double duty as a marinade and a finishing sauce. I like tasting it as I go to adjust the sweetness or tang to my liking.
I season the chicken breasts with salt and pepper, then sear them in olive oil over medium-high heat for about 5 to 6 minutes per side. In the last minute of cooking, I brush on half the mustard glaze so it caramelizes slightly on the surface. I let the chicken rest before slicing.
Using the same skillet, I toss in the broccoli and zucchini with a little more olive oil. I let them cook for about 5 minutes, stirring occasionally, until the broccoli turns bright green and the zucchini gets lightly golden. Scraping up the browned bits from the chicken adds even more flavor here.
I spoon a generous scoop of mashed potatoes into each bowl, then arrange the sliced chicken and sautéed vegetables on top. I drizzle the remaining mustard glaze over everything and finish with a sprinkle of fresh green onions. Serve it warm right away for the best texture.