Heat olive oil in a large skillet over medium-high heat. Season chicken with salt, pepper, and herbs. Sear until just cooked through, 2 to 3 minutes per side. Transfer to a plate and loosely tent with foil.
Reduce heat to medium. Add broccoli with a pinch of salt and sauté 1 to 2 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
Add orzo to the skillet and toast for 1 minute. Pour in chicken bone broth, scraping up browned bits. Bring to a gentle simmer, cover, and cook, stirring occasionally, until orzo is tender and saucy, 7 to 9 minutes. Stir in tomatoes and capers.
Lower heat and gently stir in pesto and cream. Nestle chicken back into the skillet; warm for 2 to 3 minutes.
Remove from heat and fold in Sweetie Drop peppers. Taste; adjust seasoning if needed.