Add the honey and Dijon mustard to a small bowl. Whisk until smooth and completely combined. Set aside.

Pat the chicken thoroughly dry with paper towels.

Place the chicken in a bowl or shallow dish. Add 2 tablespoons olive oil, cayenne pepper, and salt, then turn the chicken until evenly coated.

Cover and refrigerate for 1 hour to allow the seasoning to flavor the meat.

Remove the chicken from the refrigerator while preheating an indoor or outdoor grill to medium-high heat.

Grill the chicken for approximately 3–5 minutes per side, depending on thickness, until browned and cooked through. Chicken should reach an internal temperature of 165°F (74°C) at its thickest point.

Alternatively, heat a nonstick skillet over medium heat and cook the chicken for approximately 3–5 minutes per side, adjusting the cooking time according to thickness.

Transfer the cooked chicken to a plate and let it rest briefly before assembling the sliders.

Lightly brush the cut sides of the slider buns with the remaining tablespoon of olive oil. Grill or toast them until lightly crisp and golden.

Spread about 1 tablespoon of honey mustard dressing over the bottom half of each bun.

Layer each bun with sliced tomato, grilled chicken, baby arugula, and a slice of aged cheddar.

Add the top buns and serve the Honey Mustard Grilled Chicken Sliders immediately while the chicken is still warm.