Whisk broth, mustard, salt, pepper and2 teaspoons flour in a small bowl until smooth.
Sprinkle both sides of the chicken with the remaining 1 tablespoon flour. Heat oil in a large nonstick skillet over medium-high heat. Cook the chicken in two batches, adjusting heat as necessary to prevent burning, until golden, about 2 minutes per side. Transfer the chicken to a plate; tent with foil to keep warm.
Increase heat to high; stir the broth mixture and add to the skillet along with snap peas, artichoke hearts and sprouted beans. Bring to a simmer, stirring constantly. Reduce heat to maintain a gentle simmer and cook until the snap peas are tender-crisp, about 3 minutes.
Return the chicken to the pan, nestling it into the vegetables, and simmer until heated through, 1 to 2 minutes. Remove from heat; stir in herbs and vinegar.
Sprouted beans, not to be confused with bean sprouts, are beans that have just barely sprouted—they look like a bean with a tiny fiber attached (rather than the more fleshy-looking sprouts commonly used in Asian cooking). Eat raw in salads or add to cooked dishes; they're an excellent source of fiber and protein. Look for them in the produce section near other sprouts.
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