Heat a medium straight-sided skillet over medium-high heat. Add the butter and melt until the bubbles subside. Sprinkle the chicken tenders evenly on both sides with 1/2 teaspoon of the salt. Add the chicken tenders to the pan in one layer. Cook the chicken until golden brown, about 4 minutes per side (don't worry about them being cooked through at this point). Remove the chicken to a plate and set aside.
Reduce the heat to medium. Add the onions and garlic to the pan along with the remaining 1/2 teaspoon salt. Cook, stirring often, until softened and beginning to caramelize, about 4 minutes. Add the rice and chile paste and toast for an additional 2 minutes. Add the milk, chicken broth, thyme, sage and Parmesan rind. Stir to combine. Nestle the chicken pieces and their juices back into the pan in the rice. Cover the pan and reduce the heat to low. Simmer for 15 minutes.
Turn off the heat and sprinkle with the peas. Cover and allow the mixture to steam for an additional 12 minutes off the heat. Remove the herbs and rind from the pan, fluff the rice with a fork and serve with grated Parmesan and a drizzle of extra-virgin olive oil.