Heat a large sauté pan over medium heat, add the oil to the pan and heat through. Add the chicken breasts and cook, working in batches if needed. Cook the chicken until just cooked through, about 6 minutes, flipping halfway through cooking. Remove to a cutting board and set aside.

Return the pan to heat, add the shallots sauté until the shallots are tender, about 6 minutes. Add the artichokes and stir to combine.

Add 2 tablespoons of the butter and allow it to melt. Stir in the flour, cooking for a minute. Stir in the milk and bring to a simmer until the mixture thickens, about 5 minutes.

Add the Asiago and Parmesan, stirring until the cheese has melted. Season to taste with salt and pepper. Working in batches, add the spinach a few handfuls at a time, stirring to combine after each addition and cooking until the spinach has wilted.

Heat a medium non-stick sauté pan over medium heat, add the remaining butter and allow to melt. Add the breadcrumbs and sauté, stirring frequently, until the breadcrumbs are golden brown, about 5 minutes.

Return the chicken to the pan, turning to coat in the sauce. Divide the spinach artichoke chicken among plates and serve topped with breadcrumbs.