Start by marinating chicken: In a bowl or in a large Ziplock bag, mix together chicken marinade ingredients: olive oil, lemon zest, lemon juice, garlic, dijon, smoked paprika, salt, and pepper. Add chicken and toss to coat. Let marinate in the fridge for about 30 minutes (and no longer than an hour).
Heat 1 tablespoon olive oil a large skillet with high sides over medium-high heat and add chicken in a single layer. Cook for 4-5 minutes per side until golden and cooked through. Transfer to a plate to rest.
Reduce skillet heat to medium and add remaining 1 tablespoon olive oil and butter. Once butter is melted, add shallot and cook for 2-3 minutes until softened.
Stir in orzo, oregano, and red pepper flakes. Cook for 1-2 minutes, stirring frequently, until orzo is lightly golden and fragrant.
Pour chicken broth into skillet, scraping up browned bits from the bottom of pan. Bring broth to a gentle simmer and cook for 8-10 minutes, stirring occasionally, until orzo is tender and most of the liquid is absorbed.
Reduce heat to low and stir in heavy cream, parmesan, and capers.
Stir in lemon juice, taste, and add salt and pepper as needed. Fold spinach into the mixture until it's just wilting.
Slice chicken and nestle into orzo. Top with more parmesan and red pepper flakes, if desired.