Toss the chicken with the paprika and a good pinch of salt and pepper. Dust it with flour.
Heat a medium skillet over medium-high heat- spray with nonstick spray (or add 1 tablespoon olive oil). Add the chicken and sear until browned on all sides, about 7 minutes total. Remove from pan and set aside.
Add a little more oil to the pan if needed, then toss in the onions and mushrooms. Saute until everything starts to brown and caramelize, 5 minutes.
Deglaze the pan with the vermouth and let it sizzle about 1 minute. Add the chicken broth, tomato paste and bay leaves. Stir to combine.
Nestle the chicken back into the pan (with its collected juices) and simmer until the chicken is cooked through and the sauce thickens a bit, 5 to 7 minutes. Stir in the yogurt and cook 2 more minutes. Add a good pinch of salt and pepper.
In the meantime, boil the egg noodles until they reach al dente (with still a bit of a bite to them). Drain.
Serve the stroganoff over a bed of noodles and garnish with parsley.