Pat chicken breasts completely dry with paper towels spending thirty seconds per breast removing all surface moisture to enable high-heat Maillard browning reaction.

Season dried chicken breasts generously on both sides with coarse sea salt and cracked black pepper allowing salt to penetrate protein structure for moisture retention.

Heat large skillet over medium-high heat for two to three minutes until pan surface is hot adding whole unsalted butter that should foam immediately and smell nutty.

Place seasoned chicken breasts into hot butter in single uncrowded layer hearing aggressive sizzle indicating Maillard reaction beginning and letting them sit undisturbed for four to five minutes developing golden-brown crust.

Flip chicken breasts using tongs and cook second side for three to four minutes until surface develops similar golden-brown coloring with internal temperature reaching approximately one hundred fifty-five degrees Fahrenheit.

Remove partially-cooked chicken from skillet and set aside on clean plate as chicken is not yet fully cooked and will finish cooking in sauce.

Add finely minced shallot to same hot skillet and stir constantly for thirty seconds scraping up all stuck brown bits at pan bottom which is pure umami fond.

Add minced fresh garlic to pan immediately and stir continuously for thirty to forty-five seconds until fragrant smelling mellow toasted garlic not burnt.

Pour low-sodium chicken stock into pan using wooden spoon to scrape and dissolve any remaining stuck fond with stock sizzling and partially evaporating concentrating flavors.

Add oil-packed sun-dried tomatoes to pan and stir to combine allowing tomatoes to begin softening and releasing concentrated flavors into liquid.

Reduce heat to low approximately one hundred sixty to one hundred seventy degrees Fahrenheit with pan just barely simmering not boiling.

Slowly pour heavy whipping cream into pan while stirring constantly pouring from height to incorporate air which helps stabilize emulsion.

Stir cream mixture gently for two to three minutes allowing cream to fully incorporate and begin reducing slightly with sauce deepening in color from sun-dried tomatoes creating rich red-orange hue.

Return partially-cooked chicken breasts to pan nestling them into sauce with chicken at least fifty percent submerged in cream sauce.

Cook gently for five to seven minutes without boiling with residual heat combined with gentle simmering bringing chicken internal temperature from one hundred fifty-five degrees to exactly one hundred sixty-five degrees.

Check chicken doneness at six-minute mark by inserting instant-read thermometer into thickest part aiming for one hundred sixty-five degrees Fahrenheit and removing immediately when temperature reached.

Taste sauce and adjust seasoning with additional salt and pepper as needed adding approximately one tablespoon fresh lemon juice to brighten flavors and cut through richness.

Remove from heat and gently stir in freshly grated Parmigiano-Reggiano cheese and fresh thyme sprigs with residual heat melting cheese into sauce creating additional umami depth.

Slice cooked chicken breasts into three-quarter inch thick pieces and arrange on serving plates.

Spoon rich cream sauce generously over everything ensuring each portion receives sun-dried tomato shards and fresh herbs.

Garnish with fresh basil leaves finely sliced scattered across just before serving with basil aromatic volatiles maximized when fresh and not exposed to heat.