Pat the chicken cubes dry with paper towels and season evenly with salt and black pepper.
Heat olive oil in a large heavy-bottomed skillet over medium-high heat until shimmering.
Add the chicken in a single layer, working in batches if necessary to avoid overcrowding the pan.
Sear the chicken for 8-10 minutes, turning occasionally, until golden brown and the internal temperature reaches 165°F (74°C).
Remove the chicken from the skillet and set aside on a clean plate.
Reduce heat to medium and add the butter to the same skillet, scraping up any browned bits from the bottom.
Whisk in the minced garlic, Dijon mustard, lemon juice, smoked paprika, and red pepper flakes.
Simmer the butter mixture for 1-2 minutes until the garlic is fragrant and the sauce is emulsified.
Stir in the fresh parsley and chives, then return the cooked chicken to the skillet.
Toss the chicken bites thoroughly to coat in the cowboy butter sauce and serve immediately.