Pat the chicken strips dry with paper towels, then season with salt and pepper on both sides. Heat butter in a large skillet over medium-high heat until foaming, then add the seasoned chicken strips in a single layer. Cook for 3-4 minutes per side until golden brown and cooked through (internal temperature should reach 165°F). Transfer to a plate to rest while you prepare the spinach mixture. While the chicken cooks, slice the honey wheat rolls horizontally and lightly toast them cut-side up in a 400°F oven for 2-3 minutes until just golden—this prevents them from getting soggy when filled.
In the same skillet (don't wash it—those browned bits add flavor), heat olive oil over medium heat and add the minced garlic. Cook for 30 seconds until fragrant, then add the chopped spinach and cook for 2 minutes, stirring occasionally, until wilted and any excess moisture has evaporated. Reduce heat to low and add the room-temperature cream cheese, breaking it into chunks as you stir. Once the cream cheese begins to soften, add the shredded Monterey Jack, red pepper flakes, and fresh lemon juice, stirring constantly until everything is melted and combined into a smooth, creamy mixture (about 2-3 minutes). I like to taste the filling at this point and adjust the seasonings—sometimes a pinch more salt makes all the difference in bringing out the spinach flavor.
Spread a generous spoonful of the creamy spinach mixture from Step 2 onto the bottom half of each toasted roll. Place one piece of cooked chicken from Step 1 on top of the spinach filling, then cap with the top half of the roll. Serve immediately while the filling is still warm and the rolls are fresh—the combination of warm chicken, creamy cheese, and soft bread is best enjoyed right away.